text:
\section{Introduction}

String theory is argued to be
a consistent theory of quantum gravity
including gauge interactions.
As such, it provides an ideal testing
ground for expectations
a general quantum-gravity theory should satisfy.
However, conversely one can try to identify
quantum-gravity features in string theory
and conjecture them to hold in general
--- this is the approach known as the swampland program.

The swampland is defined as the set
of consistent
effective quantum field theories which cannot be completed
into consistent theories of quantum gravity
\cite{Vafa:2005ui}. During the last years there
has been an immense effort in pursuing
the swampland program and in proposing
and testing swampland conjectures.
It is not possible to give an overview of
the corresponding literature here, and
we therefore want to
refer to the review article
\cite{Palti:2019pca}.
There are however three conjectures
which play a role for this paper:
these are
 the weak gravity conjecture in its original
form \cite{ArkaniHamed:2006dz}
and the weak gravity conjecture with scalar fields
\cite{Palti:2017elp};
 the swampland distance conjecture
\cite{Ooguri:2006in} in its refined version
\cite{Klaewer:2016kiy};
and the emergence proposal
\cite{Grimm:2018ohb} which has been
further developed in \cite{Palti:2019pca}.
These conjectures will be stated in
section~\ref{sect_swampconj}.

The swampland program typically does not
rely on supersymmetry, but many
 computations in string theory
are simplified considerably when
some amount of supersymmetry is preserved.
A well-established setting is that of
type IIB string theory compactified on Calabi-Yau
three-folds $\mathcal X$, for which
the resulting
theory in four dimensions is $\mathcal N=2$
supersymmetric. The massless spectrum
is determined by the topology of the
compact space, in particular, the
four-dimensional theory contains
one gravity multiplet, $h^{2,1}$ vector multiplets
and $h^{1,1}+1$ hypermultiplets where
$h^{2,1}$ and $h^{1,1}$ denote the non-trivial
Hodge numbers of $\mathcal X$.
In such compactifications one
obtains a variety of BPS objects which have
special properties and features,
given for instance by D-branes wrapping
cycles of the compact space.
The authors of \cite{Grimm:2018ohb}
consider such type IIB compactifications
and focus on the vector-multiplet sector, which
contains closed-string $U(1)$ gauge fields and the
complex-structure moduli of $\mathcal X$.
The relevant BPS objects are D3-branes
wrapping three-cycles of the Calabi-Yau manifold,
and they are charged under the
$U(1)$s and their mass depends
on the complex-structure moduli.
For this setting many explicit checks
of various swampland conjectures have been
performed and the inter-dependence of
some of these conjectures has been illustrated.

The main question we want to ask in
this paper is
\textit{What happens to the $\mathcal N=2$
analysis when we perform
an orientifold projection?}
It is well-known that under an
orientifold projection (giving rise to O3- and O7-planes)
the $h^{2,1}$ vector multiplets of
$\mathcal N=2$ are projected to
$h^{2,1}_-$ chiral multiplets
and $h^{2,1}_+$ vector multiplets of
four-dimensional $\mathcal N=1$ supergravity
\cite{Grimm:2004uq}. In particular, we have
\eq{
  \label{multiplets_split}
  \renewcommand{\arraystretch}{1.6}
  \arraycolsep15pt
  \begin{array}{ccl}
  \mathcal N=2 &&
  \hfill\mathcal N=1\hfill
  \\
  \hline
  \multirow{2}{*}{\mbox{$h^{2,1}$ vector multiplets}}
  &
  \multirow{2}{*}{$\xrightarrow{\hspace{5pt}{\rm orientifold}\hspace{5pt}}$}
  & \mbox{$h^{2,1}_-$ chiral multiplets}
  \\
  && \mbox{$h^{2,1}_+$ vector multiplets}
  \end{array}
}
where $h^{2,1}=h^{2,1}_-+h^{2,1}_+$. Note that the $\mathcal N=1$ chiral multiplets
contain the complex-structure moduli
and the $\mathcal N=1$ vector multiplets
contain the $U(1)$ gauge fields, and
that both multiplets are independent of
each other.
As we will argue, this implies that
D3-branes wrapping three-cycles are
no longer BPS but split into massive-uncharged and massless-charged states in the four-dimensional
theory.
Hence, a priori the  analysis of \cite{Grimm:2018ohb} no longer applies.

We now want to briefly mention some works in the
literature which are  related to
our discussion:
\begin{itemize}

\item As discussed above, the work
of \cite{Grimm:2018ohb} studies swampland
conjectures for $\mathcal N=2$ compactifications
of type IIB string theory.
Here we perform an analysis for the
theory obtained after an orientifold projection
to $\mathcal N=1$.

\item In \cite{Font:2019cxq} the authors
investigate (among others)
domain walls in $\mathcal N=1$
orientifold compactifications of
type II string theory. For the O3-/O7-situation, these domain walls are given by D5-branes
wrapping three-cycles of the Calabi-Yau manifold.
The mass of these four-dimensional states
is determined by the complex-structure
moduli and they are charged under
closed-string three-form gauge fields, but not
under closed-string one-form gauge fields.

\end{itemize}

This paper is organized as follows: in section~\ref{sec_iiborientifolds} we review type IIB orientifold compactifications with
orientifold three- and seven-planes, and
in section~\ref{sec_d3} we analyze
D3-branes wrapping three-cycles in the
compact space. In section~\ref{sect_swampconj} we discuss the weak gravity conjecture, the
swampland distance conjecture and the
emergence proposal for this setting,
and section~\ref{sect_conc} contains
our summary and conclusions.
We furthermore mention that this paper is based on the master thesis \cite{martin:2019}
of one of the authors,
where further details and discussions can
be found.

\section{Type IIB orientifolds}
\label{sec_iiborientifolds}

In this section we briefly review Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. We consider the general situation with $h^{2,1}_+\neq0$,
leading to closed-string $U(1)$ gauge fields
in the four-dimensional effective theory \cite{Grimm:2004uq}.

\subsection{Calabi-Yau orientifolds}
\label{sec_orientifolds}

We start by introducing our notation for the topology of Calabi-Yau orientifolds,
and we provide some details on the special geometry of the complex-structure moduli space.

\subsubsection*{Topology}

We consider a Calabi-Yau three-fold $\mathcal X$,
which comes with a  holomorphic three-form $\Omega\in H^{3,0}(\mathcal X)$ and a
real K\"ahler form $J\in H^{1,1}(\mathcal X)$.
To perform an orientifold projection we impose
a holomorphic involution
$\sigma$ on $\mathcal X$, chosen to act on $\Omega$ and $J$ as
\eq{
  \label{orient_choice}
  \sigma^*J=+J\,,\hspace{60pt}
  \sigma^*\hspace{1pt}\Omega=-\Omega\,.
}
Since $\sigma$ is an involution,
the cohomology groups of the Calabi-Yau three-fold $\mathcal X$ split into even and odd
eigenspaces as $H^{p,q}(\mathcal X) = H^{p,q}_+(\mathcal X) \oplus
H^{p,q}_-(\mathcal X)$ with dimensions $h^{p,q}_+$ and $h^{p,q}_-$.
Of interest to us will be the third de-Rham cohomology group
$H^3(\mathcal X)= H^{3}_+(\mathcal X) \oplus
H^{3}_-(\mathcal X)$, for which we choose a symplectic basis in the following way
\begin{align}
  &\label{basis_01}
  \arraycolsep2pt
  \begin{array}{l@{\hspace{40pt}}lcl@{\hspace{40pt}}lcl}
  \raisebox{-20pt}[0pt][-20pt]{$\displaystyle \{\alpha_I ,\alpha_a, \beta^I,\beta^a \}\,,$}
  &
  \displaystyle \int_{\mathcal X} \alpha_{I} \wedge \beta^J &=& \displaystyle \delta_I{}^J \,,
  &
  \displaystyle I,J &=& \displaystyle 0,\ldots, h^{2,1}_- \,,
  \\[16pt]
  &
  \displaystyle \int_{\mathcal X} \alpha_{a} \wedge \beta^b &=& \displaystyle \delta_a{}^b \,,
  &
 \displaystyle a,b &=& \displaystyle 1,\ldots, h^{2,1}_+ \,,
 \end{array}
 \\
\intertext{
with all other pairings vanishing.
A corresponding basis of the third homology group
$H_3(\mathcal X)= H_{3+}(\mathcal X) \oplus
H_{3-}(\mathcal X)$
together with the non-trivial pairings takes the form
}
  &\label{basis_02}
  \arraycolsep2pt
  \begin{array}{l@{\hspace{34pt}}lcl@{\hspace{62pt}}lcl}
  \raisebox{-20pt}[0pt][-20pt]{$\displaystyle \{A^I ,A^a, B_I,B_a \}\,,$}
  &
  \displaystyle \int_{A^I} \alpha_{J} &=& \displaystyle \delta^I{}_J \,,
  &
  \displaystyle \int_{B_I} \beta^{J} &=& \displaystyle \delta_I{}^J \,,
  \\[16pt]
  &
  \displaystyle \int_{A^a} \alpha_{b} &=& \displaystyle \delta^a{}_b \,,
  &
  \displaystyle \int_{B_a} \beta^{b} &=& \displaystyle \delta_a{}^b \,.
  \end{array}
\end{align}

\subsubsection*{Special geometry}

Next, we consider the special geometry of the complex-structure moduli space.
The holomorphic three-form $\Omega$ can be expanded in the symplectic basis
\eqref{basis_01}
as follows
\eq{
  \Omega = X^I \alpha_I - F_I\hspace{1pt} \beta^I \,.
}
Since $\Omega$ is odd under the orientifold projection -- cf.~equation \eqref{orient_choice} -- the coefficients of $\Omega$
in the even basis $\{\alpha_a,\beta^a\}$ are vanishing, that
is $X^a=0$ and $F_a\rvert_{X^a=0}=0$. We will refer to these conditions also as the orientifold locus
and discuss them in more detail below. The complex-structure moduli are coordinates on a projective space and are usually defined
as
\eq{
  z^i = \frac{X^i}{X^0}
  \,, \hspace{40pt} z^i= u^i + i\hspace{1pt} v^i
  \,, \hspace{40pt} i = 1, \ldots, h^{2,1}_- \,,
}
and we note that in our conventions the large-complex-structure limit corresponds to $v^i\to\infty$.
For Calabi-Yau compactifications the periods $F_I$ can be defined in terms of a prepotential $F$ which is a
holomorphic function of degree two in the fields $X^{\mathsf I} = (X^I,X^a)$.
More concretely, the $F_I$ are defined as the derivatives
\eq{
  F_I = \frac{\partial F}{\partial X^I} \biggr\rvert_{X^a=F_a=0} \,,
}
which in our present setting have to be evaluated at the orientifold locus.
The prepotential $F$ of the $\mathcal N=2$ theory  consists of a tree-level part involving the triple intersection numbers
$d_{\mathsf{ijk}}$ of the mirror Calabi-Yau manifold and one-loop and non-perturbative
corrections. More concretely, we have \cite{Hosono:1994av,Hosono:1994ax}
\eq{
\label{prepotential_full}
F=
\arraycolsep2pt
\begin{array}[t]{cl}
&\displaystyle \frac{d_{\mathsf{ijk}} X^{\mathsf i}X^{\mathsf j}X^{\mathsf k}}{X^{0}}
\\[8pt]
+&\displaystyle  \frac{1}{2}\hspace{1pt} a_{\mathsf {ij}}X^{\mathsf i}X^{\mathsf j}+b_{\mathsf i}\hspace{1pt} X^{\mathsf i}X^{0}
+\frac{1}{2}\hspace{1pt} c\hspace{1pt} (X^{0})^2
+ i\hspace{1pt} (X^{0})^2\sum_{k}n_{k}\text{Li}_{3}\Bigl(e^{2\pi i\hspace{1pt} k_{\mathsf i}X^{\mathsf i}/X^{0}}\Bigr) \,,
\end{array}
}
where the indices $\mathsf{i},\mathsf{j},\mathsf{k}=1,\ldots, h^{2,1}$ extend over the even and odd cohomology,
$a_{\mathsf{ij}}$ and $b_{\mathsf i}$ are rational real numbers whereas $c$ is purely imaginary.\footnote{These numbers encode the one-loop corrections.
We note that there is an ambiguity related to them:
for certain non-singular cases they have been
computed in \cite{Hosono:1994ax} but
to our knowledge these are not known
for singular configurations.\label{foot_oneloop}}
The triple intersection numbers $d_{\mathsf{ijk}}$ and the $a_{\mathsf{ij}}$ are symmetric in their indices,
$n_{k}$ are the genus zero Gopakumar-Vafa invariants, ${\rm Li}_3$ denotes the third poly-logarithm and
$k_{\mathsf i}$ are the wrapping numbers of
world-sheet instantons along two-cycles of
the mirror Calabi-Yau.

\subsubsection*{Orientifold locus}
\label{page_or_loc}

From the $\mathcal N=2$ perspective the orientifold locus
is determined by $X^a=0$, $F_a=0$ for all $a=1,\ldots, h^{2,1}_+$.
The condition $X^a$ alone describes
a conifold singularity in which an $A$-cycle
shrinks to zero size, and the physics
of conifold singularities
is well understood \cite{Strominger:1995cz}.
However, imposing in addition $F_a=0$
means that also the dual $B$-cycle vanishes.
We are not aware of work in the
literature studying such situations and we
continue with a heuristic discussion.

Let us then study in more
detail the condition
$F_a=0$ evaluated at $X^a=0$.
From the explicit form of
\eqref{prepotential_full} we determine
\eq{
  \label{period_ll}
  F_a
   = X^0 \left[ 3 \hspace{1pt} d_{aij} z^i z^j
  + a_{ai} z^i + b_a
  - 2\pi
  \sum_{k} k_a n_{k}\text{Li}_{2}\Bigl(e^{2\pi i\hspace{1pt} k_{i}z^{i}}\Bigr)
  \right],
}
where we recall that $i,j=1,\ldots, h^{2,1}_-$ and
$a=1,\ldots, h^{2,1}_+$.
Requiring $F_a=0$ for all $z^i$
can be solved in the following two ways:
\begin{enumerate}
\label{page_or_sol}

\item A sufficient set of conditions for
the periods $F_a$  to vanish for all $z^i$
reads
\eq{
  \label{or_sol_1}
  d_{aij} = 0 \,, \hspace{40pt}
  a_{ai} = 0 \,, \hspace{40pt}
  b_{a} = 0 \,, \hspace{40pt}
  k_{a} = 0 \,.
}
However, especially the condition $k_a=0$ is
rather restrictive since it means that
all world-sheet instanton corrections in
the orientifold-even sector have to be absent.
This in turn implies a discrepancy
in our discussion of emergence in section~\ref{emergencesect}.

\item A second possibility is to require a
splitting of the
sum over $k$ in \eqref{period_ll} into
purely odd and purely even vectors as
$
  \sum_{k} = \sum_{k_i} + \sum_{k_a}
$.
Using then the relation
$\text{Li}_2(1) = \pi^2/6$ we find
the conditions
\eq{
  \label{or_sol_2}
  d_{aij} = 0 \,, \hspace{40pt}
  a_{ai} = 0 \,, \hspace{40pt}
  b_{a} = \frac{\pi^3}{3} \sum_{k_a} k_a n_k \,.
}
It is not clear to us whether the last of
these conditions can be satisfied,
but we mentioned in footnote~\ref{foot_oneloop} that there is an ambiguity for the
one-loop coefficients.
The solution \eqref{or_sol_2} however
realizes $F_a=0$ with  $k_a\neq0$
which is needed
for our discussion in section~\ref{emergencesect}.

\end{enumerate}

\subsection{Effective action}

We now turn to the effective four-dimensional action obtained after compactifying
type IIB string theory on the Calabi-Yau orientifolds described above.
The details of this action can be found in the literature,
and here we focus on the sector corresponding to the third cohomology of $\mathcal X$.

\subsubsection*{Moduli}

We compactify type IIB string theory on a Calabi-Yau three-fold
as $\mathbb R^{3,1}\times \mathcal X$ and perform an orientifold projection.
The orientifold projection is of the form
$\Omega_{\rm P} (-1)^{F_{\rm L}} \sigma$, where
$\Omega_{\rm P}$ denotes the world-sheet parity operator and $F_{\rm L}$ is
the left-moving fermion number.
The holomorphic involution $\sigma$ acts on $\mathcal X$ as in
\eqref{orient_choice} and
leaves the non-compact four-di\-men\-sional part invariant. Hence,
the fixed loci of $\sigma$ correspond to orientifold three- and seven-planes.
The combination $\Omega_{\rm P} (-1)^{F_{\rm L}}$ acts on the massless bosonic fields
in the following way
\eq{
  \label{orient_signs}
  \arraycolsep2pt
  \begin{array}{lclclcl}
  \arraycolsep1.5pt
  \displaystyle \Omega_{\rm P}\, (-1)^{F_{\rm L}}\: g &=& + \:g \,,  & \hspace{60pt} &
  \displaystyle \Omega_{\rm P}\, (-1)^{F_{\rm L}}\: B &=& - B \,, \\[6pt]
  \displaystyle \Omega_{\rm P}\, (-1)^{F_{\rm L}}\: \phi &=& + \:\phi \,,  & \qquad &
  \displaystyle \Omega_{\rm P}\, (-1)^{F_{\rm L}}\: C_{2p} &=& (-1)^{p}
    \,C_{2p} \,,
  \end{array}
}
with $g$ the metric, $B$ the Kalb-Ramond field, $\phi$ the dilaton and
$C_{2p}$ the Ramond-Ramond (R-R) potentials in type IIB.
The degrees of freedom contained in these fields
become fields in the compactified theory, in particular, the deformations of the
Calabi-Yau metric are contained in the K\"ahler form $J$ and the holomorphic three-form $\Omega$.
For the Ramond-Ramond four-form potential we note that $C_4$ can be expanded  as
\begin{align}
  \label{expansion_001}
  C_4 = C_4^{(0,4)} +{} &C_4^{(1,3)} + C_4^{(2,2)} + C_4^{(4,0)} \,,
  \\[2pt]
  \nonumber
  &\hspace{4pt}\downarrow
  \\[2pt]
  \nonumber
  &C_4^{(1,3)} = U^a\wedge  \alpha _a + V_a\wedge \beta^a \,,
\end{align}
where in $C_4^{(m,n)}$ the superscript $m$ denotes the degree in four dimensions and $n$ the
degree on the compact space $\mathcal X$.
Note furthermore that $U^a$ and $V_a$ correspond to $U(1)$ vector fields in four dimensions.
The four-form \raisebox{0pt}[0pt][0pt]{$C_4^{(4,0)}$} in $\mathbb R^{3,1}$ is not dynamical, and
due to the self-duality conditions imposed on $C_4$ half of the degrees of freedom in the expansion
\eqref{expansion_001}
are removed. Here we choose to remove \raisebox{0pt}[0pt][0pt]{$C_4^{(2,2)}$} and $V_a$ but keep
\raisebox{0pt}[0pt][0pt]{$C_4^{(0,4)}$} and $U^a$, respectively.
The four-dimensional massless fields (in addition to the four-dimensional metric $g_{\mu\nu}$) then take the following schematic
form
\eq{
  \renewcommand{\arraystretch}{1.2}
  \arraycolsep2pt
  \begin{array}{l@{\hspace{40pt}}lcl@{\hspace{10pt}}c@{\hspace{10pt}}l}
  \mbox{complex-structure moduli} & \multicolumn{3}{@{}l}{\Omega}   & \longleftrightarrow & H^{3}_-(\mathcal X)\,,
  \\
  \mbox{$U(1)$ vector fields} & \multicolumn{3}{@{}l}{C_4^{(1,3)}}  & \longleftrightarrow & H^{3}_+(\mathcal X)\,,
  \\[6pt]
  \mbox{K\"ahler moduli} & J &+& C_4^{(0,4)} & \longleftrightarrow & H^{2,2}_+(\mathcal X)\,,
  \\
  \mbox{odd moduli} & B &+& C_2 & \longleftrightarrow & H^{1,1}_-(\mathcal X)\,,
  \\
  \mbox{axio-dilaton} & \phi &+& C_0 & \longleftrightarrow & H^{0,0}_+(\mathcal X)\,.
  \end{array}
}

\subsubsection*{Four-dimensional action}

Compactifications of type II string theory on Calabi-Yau manifolds lead to a $\mathcal N=2$
supergravity theory in four dimensions, which can be
reduced to $\mathcal N=1$ by an orientifold projection.
Here we are interested in the action corresponding to the complex-structure moduli $z^i$ and the vector fields
$U^a$, which can be brought into the following  general form
\eq{
  \label{action_001}
  \mathcal S \supset
   \frac{1}{2}\int_{\mathbb R^{3,1}} \,\Bigl[ \;
  -\mbox{Re}\hspace{1pt} (f_{ab}) \hspace{1pt} F^a\wedge \star F^b
  +\mbox{Im}\hspace{1pt} (f_{ab}) \hspace{1pt} F^a\wedge  F^b
  - 2\hspace{1pt} G_{i\overline j} \, dz^i \wedge\star d\overline z{}^{\overline j} \;\Bigr]\,.
}
The K\"ahler metric $G_{i\overline j}$ for the complex-structure moduli $z^i$ appearing in the
action \eqref{action_001} is computed from a K\"ahler potential $K_{\rm cs}$ as
\eq{
  \label{metric_k}
  G_{i\overline j} = \frac{\partial^2 K_{\rm cs}}{\partial z^i \partial \overline z{}^{\overline j}}\biggr\rvert_{X^c=F_c=0} \,,
  \hspace{50pt}
  K_{\rm cs} &= - \log \Bigl[\, - i\int_{\mathcal X} \Omega\wedge \overline\Omega\:\Bigr] \,,
}
and the $U(1)$ field strength corresponding to $U^a$ is denoted by $F^a = dU^a$.
The gauge kinetic function $f_{ab}$ can be expressed in terms of the period matrix
$\mathcal N$ as
\eq{
  \label{period_m_001}
  &f_{ab} = -i \hspace{1pt}\overline{\mathcal  N}_{ab}\,,
  \\
  &\mathcal N_{ab}=\overline{F}_{ab}+2\hspace{1pt} i \, \frac{
{\rm Im}(F_{aI}) X^I \, {\rm Im}(F_{bJ}) X^J}{
           X^M \hspace{1pt}{\rm Im}(F_{MN}) X^N}=\mathcal{R}_{ab}+i\,\mathcal{I}_{ab}  \,,
}
which follows from evaluating the $\mathcal N=2$ gauge kinetic function
on the orientifold locus $X^a=0$, $F_a=0$ \cite{Grimm:2004uq}.
The period matrix in \eqref{period_m_001} is written using second derivatives of the prepotential $F$, that is
\eq{
\label{derivatives_001}
F_{\mathsf{IJ}} = \frac{\partial^2 F}{\partial X^{\mathsf I}\partial X^{\mathsf J}} \biggr\rvert_{X^c=F_c=0} \,,
\hspace{50pt}
\mathsf I,\mathsf J = 0, \ldots, h^{2,1}\,.
}

\subsubsection*{Some expressions}

We finally collect some technical results.
We first define the inverse of the real part of the gauge kinetic function
as the $\mathcal N=2$ expression restricted to the orientifold locus,
and we obtain using \eqref{derivatives_001} that
\eq{
 \bigl[(\mbox{Re}\hspace{1pt} f)^{-1} \bigr]^{ab} = - \bigl[ (\mbox{Im}\hspace{1pt} F)^{-1} \bigr]^{ab}\,.
}
Second, for the $\mathcal N=2$ setting
one usually defines a $(2h^{2,1}+2)\times(2h^{2,1}+2)$ dimensional matrix $\mathcal M$
which corresponds to a metric for the third cohomology. We are interested
in the orientifold-even part evaluated on the orientifold locus
which takes the form
\eq{
\label{matrix_m}
 \mathcal M = \left( \begin{array}{cc}
-\bigl[ ({\rm Im}\hspace{1pt}\mathcal N)^{-1}\bigr]^{ab}
&
 \bigl[ ({\rm Im}\hspace{1pt}\mathcal N)^{-1}( {\rm Re}\hspace{1pt}\mathcal N )\bigr]^a_{\hspace{4pt}b}
\\[4pt]
 \bigl[ ( {\rm Re}\hspace{1pt}\mathcal N )({\rm Im}\hspace{1pt}\mathcal N)^{-1}\bigr]_a^{\hspace{4pt}b}
&
 -\bigl[(  {\rm Im}\hspace{1pt}\mathcal N) +( {\rm Re}\hspace{1pt}\mathcal N )({\rm Im}\hspace{1pt}\mathcal N)^{-1}( {\rm Re}\hspace{1pt}\mathcal N)\bigr]_{ab}
  \end{array}
  \right),
}
with $a,b=1,\ldots, h^{2,1}_+$. Note that this matrix is positive definite.
The separate blocks of \eqref{matrix_m} can be determined in terms of
\eqref{derivatives_001} and take the following form
\eq{
 \bigl[ ({\rm Im}\hspace{1pt}\mathcal N)^{-1}\bigr]^{ab}  & = - \bigl[ ({\rm Im}\hspace{1pt} F)^{-1}\bigr]^{ab} \,,
 \\
 \bigl[ ( {\rm Re}\hspace{1pt}\mathcal N )({\rm Im}\hspace{1pt}\mathcal N)^{-1}\bigr]_a^{\hspace{4pt}b}  & = - \bigl[ ({\rm Re}\hspace{1pt} F)({\rm Im}\hspace{1pt} F)^{-1}\bigr]_a^{\hspace{4pt}b} \,,
 \\
 \hspace{-5pt}
 \bigl[(  {\rm Im}\hspace{1pt}\mathcal N) +( {\rm Re}\hspace{1pt}\mathcal N )({\rm Im}\hspace{1pt}\mathcal N)^{-1}( {\rm Re}\hspace{1pt}\mathcal N)\bigr]_{ab}
 & = -  \bigl[ ( {\rm Im}\hspace{1pt} F) +( {\rm Re}\hspace{1pt} F)({\rm Im}\hspace{1pt} F)^{-1}( {\rm Re}\hspace{1pt} F)\bigr]_{ab}  \,.
 \hspace{-20pt}
}

\section{D3-branes wrapping three-cycles}
\label{sec_d3}

The main objects of interest for our analysis
are D3-branes wrapping three-cycles
in the compact geometry, which  give
rise to particles in the four-dimensional
theory.

\subsection{D-branes}

For our purpose we are looking for  objects which are charged under the $U(1)$ gauge fields $U^a$.
Since the $U^a$ are contained in the expansion \eqref{expansion_001} of the R-R four-form $C_4$,
we are focussing on D-branes.

\subsubsection*{D3-branes}
\label{d3bra}

We first want to show that for the setting introduced above, the only objects coupling directly to
the closed-string gauge fields are D3-branes wrapping three-cycles in the
compact space.\footnote{As discussed for instance in \cite{Jockers:2005pn,Marchesano:2014bia}, the closed-string $U(1)$ gauge fields can also couple to open-string moduli. This situation is however not generic and will therefore be ignored in the following.}
To do so, we  recall the Chern-Simons part of the D-brane action.
With $\mu_p$ its charge, $\Gamma$ the submanifold wrapped by the D-brane,
$\mathcal F$ the open-string gauge invariant
field strength and the $\hat{\mathcal{A}}$-genus of the curvature two-form, we have
\eq{
  \mathcal{S}_{{\rm D}p} &\supset -\mu_p \int_{\Gamma}
    \mbox{ch}\left( \mathcal F\right) \wedge
    \sqrt{ \frac{\hat{\mathcal A}(\mathcal R_T)}{\hat{\mathcal A}(\mathcal R_N)}} \wedge
    \bigoplus_q C_q \,.
}
Since $ \mbox{ch}\left( \mathcal F\right)$ as well as the $\hat{\mathcal{A}}$-terms are even forms,
and since on a Calabi-Yau manifold the first and fifth cohomology are trivial, the only
possible D-branes which couple to $C^{(1,3)}$ (cf.~the expansion in \eqref{expansion_001})
have to wrap  (orientifold-even)  three-cycles in $\mathcal X$.
Furthermore, since $\mathcal F$ is odd under $ \Omega_{\rm P}\, (-1)^{F_{\rm L}}$
the four-dimensional part does not contain $\mathcal F$ and we arrive
at a D3-brane wrapping a three-cycle in the compact space $\mathcal X$.
That means, we consider D3-branes extending along the time direction in
the non-compact four-dimensional space $\mathbb R^{3,1}$ and wrapping
three-cycles $\Gamma_3\subset\mathcal X$, where the latter can be expanded
in the basis \eqref{basis_02} as follows
\eq{
  \Gamma_3 = m_I A^I + m_a A^a + n^I B_I + n^a B_a\,.
}

\subsubsection*{Supersymmetry}

The orientifold three- and seven-planes typically present in the
background preserve a particular combination of
the $\mathcal N=2$ supercharges in the four-dimensional theory,
leading to $\mathcal N=1$.
However, D3-branes wrapping three-cycles in the compact space
 break supersymmetry further.
Using  the $\kappa$-symmetry formalism for D-branes
and following the
analysis of \cite{Bergshoeff:1996tu,Bergshoeff:1997kr,Marino:1999af,Kachru:1999vj},
we find the following:
\begin{itemize}
\label{page_susy}
\item A D3-brane wrapping an orientifold-even three-cycle $\Gamma_3\in H_{3+}(\mathcal X)$ breaks
supersymmetry completely.
The volumes of such three-cycles are expected to vanish,
in agreement with the classification of
toroidal orientifolds in
\cite{Lust:2006zh} where the $h^{2,1}_+$ sector belongs to the twisted sector. Alternatively,
this conclusion is reached by projecting
the $\mathcal N=2$ expression to
$\mathcal N=1$.

\item A D3-brane wrapping an orientifold-odd three-cycle $\Gamma_3\in H_{3-}(\mathcal X)$ preserves
at most one-half of the $\mathcal N=1$ supersymmetry in four dimensions, that is,
such a D3-brane preserves at most two real supercharges.
To do so, a calibration condition of the following form has to be satisfied
\eq{
  \label{calibration_001}
  \mbox{Re}\bigl(e^{i\hspace{1pt}\theta} \Omega\hspace{1pt}\bigr)\bigr\rvert_{\Gamma_3} = e^{-K_{\rm cs}/2}\,d\mbox{vol}(\Gamma_3) \,,
  \hspace{40pt}
  \mbox{Im}\bigl(e^{i\hspace{1pt}\theta} \Omega\hspace{1pt}\bigr)\bigr\rvert_{\Gamma_3}   =0\,,
}
where $\theta\in\mathbb R$ is an arbitrary phase. It has to be equal for all
such D3-branes present in the background.\footnote{
For space-time filling D-branes the angle $\theta$ is typically
fixed
by comparing with corresponding orientifold planes, but
such a mechanism is not available here.}

\end{itemize}
The important point is that D3-branes wrapping three-cycles in
the Calabi-Yau orientifold do not preserve the same supersymmetry
as the orientifold three- and seven-planes. In particular, they are
not BPS and hence the usual stability arguments do not apply ---
in general such states are therefore unstable. We come back to this
point in section~\ref{sec_stability} below.

Our findings above are consistent with the projection
of the $\mathcal N=2$ BPS condition
for Calabi-Yau compactifications.
More concretely, D3-branes wrapping three-cycles in Calabi-Yau
three-folds are known to satisfy the inequality \cite{Becker:1995kb}
\eq{
\text{Vol}(\Gamma_{3})\geq e^{K_{\rm cs}/2}
\left| \int_{\Gamma_{3}}\Omega\hspace{1pt}\right|  ,
\label{eq:ineqBBS}
}
where the equality corresponds to BPS states in the
$\mathcal N=2$ theory.
When projecting this condition to $\mathcal N=1$
via the orientifold
projection, we expect  corrections to the
relation \eqref{eq:ineqBBS}.
However, our expectancy is that these are under control in the large complex-structure regime.
Furthermore, since these D3-branes wrap topologically non-trivial
cycles in the Calabi-Yau orientifold while being non-BPS,
the backreaction on the geometry should be taken into account.

\subsubsection*{Four-dimensional particles}

D3-branes wrapping three-cycles in the compact space can be interpreted as particles in the
four-dimensional non-compact theory.
The DBI-part of a D-brane action with $\mathcal F=0$ has the form
$\mathcal S_{{\rm D}p}\supset - T_p \int_{\Gamma} e^{-\phi}\hspace{1pt} d\mbox{vol}$, where $T_p$ denotes
the tension of the brane. Going then to Einstein frame
we find the following action
for D3-branes wrapping $\Gamma_3$
\eq{
  \label{action_redux_001}
  \mathcal S_{{\rm D}3} &= - T_3 \int_{\mathbb R \times \Gamma_3}
  ds\wedge \text{dvol}(\Gamma_3)
  - \mu_3 \int_{\mathbb R \times \Gamma_3}  C_4
  \\[4pt]
  &\sim - m \int_{\mathbb R}
  ds
    -  \int_{\mathbb R} \bigl(m_a \hspace{1pt} U^a + n^a\hspace{1pt} V_a\bigr) \,,
}
where  $ds$ is the line element of the world-line in four dimensions. We also included electric as well as magnetic couplings of the D3-brane to the gauge fields and we combine
the corresponding charges into the vector $\mathfrak q=(m_a,n^a)$.
Depending on whether the D3-brane wraps an
orientifold-even or an orientifold-odd
three-cycle, we find the following two classes of particles:
\begin{itemize}

\item D3-branes wrapping odd three-cycles $\Gamma_3 \in H_{3-}(\mathcal X)$ give rise
to massive particles in four dimensions. These are not charged under the $U(1)$ gauge symmetries and therefore are in general unstable.
Using \eqref{action_redux_001} and the equality in \eqref{eq:ineqBBS} we can then read-off the mass
(in units $\sqrt{8\pi} M_{\rm Pl}$) and charges of these particles as
\eq{
\label{d3_odd}
  m = e^{K_{\rm cs}/2}
   \Bigl|m_IX^I - n^IF_I \Bigr|  + \ldots
  \,,
  \hspace{40pt} \mathfrak q = 0
  \,,
 }
  where $\ldots$ correspond to the aforementioned corrections in the orientifold setting which we expect are subleading in the large complex-structure limit.

\label{page_masses_d3}

\item D3-branes wrapping even three-cycles $\Gamma_3 \in H_{3+}(\mathcal X)$  give rise to massless four-dimensional particles.
This can be explained by noting that explicit constructions of orientifold-even three-cycles in type IIB orientifolds belong to the twisted sector and have vanishing volume \cite{Lust:2006zh}, or alternatively by projecting the $\mathcal N=2$ result.
However, these massless particles
are charged under the $U(1)$ gauge symmetries
with electric charge $m_a$ and magnetic charge
$n^a$, that is
\eq{
  \label{d3_even}
  m = 0 \,, \hspace{40pt}
  \mathfrak q = \binom{m_a}{n^a}\,.
}

\end{itemize}
D3-branes wrapping a general three-cycle can of course be massive as well as charged,
but in these cases the $U(1)$ charges and their masses are not related to each other.

\subsection{Stability}
\label{sec_stability}

Above we have argued
that D3-branes wrapping
three-cycles in the compact space
do not preserve the same supersymmetry as
the orientifold three- and seven-planes.
They are therefore not
BPS states of the four-dimensional theory
and thus in general unstable.

\subsubsection*{D3-branes wrapping orientifold-odd three-cycles}

Let us start by briefly recalling the $\mathcal N=2$ situation. In this case, D3-branes wrapping special-Lagrangian three-cycles in the
compact space
give rise to BPS states of the
four-dimensional theory.
Such states feel an equilibrium
of repulsive (gauge interactions) and
attractive (gravitational and
scalar interactions) forces,
which allows them to be stable.
Furthermore, there can be
infinite towers of BPS states as they do not feel a force among themselves. Nevertheless, in order to avoid decay by marginal stability the authors of  \cite{Grimm:2018ohb} use a monodromy-orbit formalism to find appropriate bound states building these towers.

In the $\mathcal N=1$ orientifold setting,
as discussed above, the gauge vectors associated to
orientifold-odd three-cycles $\Gamma_3 \in H_{3-}(\mathcal X)$ are projected out.
The D3-branes wrapping such cycles
are massive but uncharged,
and therefore feel an  attractive potential which usually manifests
itself via a tachyonic mode and subsequent tachyon condensation and decay \cite{Sen:1999mg,Sen:1999nx}. This is in resemblance to the D-brane of the bosonic string \cite{Sen:1999mg,Sen:1999nx}, but in our case the spatial extension of the brane is wrapping three-cycles of the Calabi-Yau manifold. As a consequence,
without a proper analysis taking into account the backreaction onto the geometry
the final state is unknown.
The same reasoning applies to towers of
such states which are again unstable, reflecting the fact that the monodromy-orbit formalism of \cite{Grimm:2018ohb} is not applicable to these uncharged D3-particles.
To summarize, D3-branes wrapping orientifold-odd three-cycles of the Calabi-Yau are in general unstable.
We make the following remarks:
\begin{itemize}

\item Around equation~\eqref{calibration_001}
we discussed that
some D3-brane configurations preserve $\mathcal{N}=1/2$ supersymmetry in four dimensions. These states might have some notion of stability, but a
proper analysis is beyond the scope of this work.

\item We are not considering non-BPS stability by means of K-theoretical discrete symmetries, since
states which are K-theoretical stable are not candidates to build towers of states.
In particular, the open-string tachyon for stable non-BPS branes on orientifolds is projected out by world-sheet parity which can only happen for a single brane, whereas  towers of more than one brane are unstable and decay \cite{Sen:1999mg}.

\end{itemize}

As we have argued,  at a generic point in complex-structure moduli space
D3-branes wrapping cycles $\Gamma_3 \in H_{3-}(\mathcal X)$ are unstable.
However, when approaching the large complex-structure limit their mass
and their scalar interactions
approach zero and these states become
``asymptotically stable''.
In particular, the imbalance of forces gets reduced and  backreaction effects become less and less relevant.
A motivation for this interpretation is the analysis of emergence for the orientifold-odd sector in section~\ref{emergencesect}.

\subsubsection*{D3-branes wrapping orientifold-even three-cycles}

D3-branes wrapping orientifold-even three-cycles $\Gamma_3 \in H_{3+}(\mathcal X)$ in the compact space
correspond to massless-charged particles in
the four-dimensional theory, which
in the context of the swampland program
have been discussed for instance in \cite{Heidenreich:2017sim,Heidenreich:2019zkl}.
Many of these particles are however unstable and
can decay into their elementary constituents, since
there is no mass associated to them. The stable states correspond to the following fundamental charges (for a fixed $a$):
\eq{
\label{states_elem}
\arraycolsep2pt
\begin{array}{lcl@{\hspace{30pt}}l}
(m_a,n^a)&=&(1,0) & \mbox{massless electric particles,}
\\[4pt]
(m_a,n^a)&=&(0,1) & \mbox{massless  magnetic monopoles.}
\end{array}
}
This reasoning is supported from the $\mathcal{N}=2$ perspective where it was argued in \cite{Strominger:1995cz} that the conifold singularity is resolved by the addition of the electric state $(m_a,n^a)=(1,0)$, while the states $(m_a,n^a)=(\mathbb Z,0)$ should decay to the previous one in order to match the one-loop beta function for the electric gauge coupling.
Since the orientifold locus $X^a=0$ resembles a
conifold singularity,
it is not surprising that we inherit these  stable states in the orientifold theory.

\subsubsection*{Remark}

We close this section be remarking that D3-branes wrapping general three-cycles can of course be massive as well as charged,
but in these cases the $U(1)$ charges and their masses are not related to each other. As a consequence, they ultimately decay to the previous cases.

\section{Swampland conjectures}
\label{sect_swampconj}

We now want to test several swampland conjectures
for particles in the setting introduced above.
These are the weak gravity conjecture,
the swampland distance conjecture and the emergence
proposal.

\subsection{Weak gravity conjecture}

We begin our discussion of swampland conjectures
with the weak gravity conjecture.

\subsubsection*{Recalling the conjectures}

We start by briefly recalling the electric weak gravity conjecture \cite{ArkaniHamed:2006dz} in its modern formulation \cite{Palti:2019pca}:
\begin{itemize}

\item[] Consider a $U(1)$ gauge theory  with gauge coupling $g$
coupled to gravity and described by the following action
\begin{equation}
\mathcal S= \frac{1}{2} \int_{\mathbb R^{3,1}} \left[
M_{\rm P}^2 \, R\star 1 - \frac{1}{2\hspace{1pt} g^2}\hspace{1pt}
F\wedge\star F + \ldots\hspace{1pt} \right],
\label{eq:actionWGC}
\end{equation}
where $R$ denotes the Ricci scalar and $F$ is the $U(1)$ field-strength two-form.
Then there exists a particle in the theory with mass $m$ and charge $\mathfrak q$ satisfying the inequality
\begin{equation}
m
\leq \sqrt{2}\hspace{1pt} \mathfrak q\hspace{1pt} g
M_{\rm P} \, .
\label{eq:eWGC}
\end{equation}

\end{itemize}
This conjecture has been refined in many ways, and for our purpose the weak gravity conjecture with scalar fields will be relevant \cite{Palti:2017elp}.
We recall this conjecture as follows:
\begin{itemize}

\item[] Consider a gravity theory with massless scalar fields $z^i$ and $U(1)$ gauge fields $U^a$ described by the
action \eqref{action_001}. Then there should exist a particle with mass $m(z)$ satisfying the bound
\begin{equation}
\label{conjecture_wg}
\mathcal{Q}^2
\geq m^2+G^{i\overline j}(\partial_{z^{i}} m)(\partial_{\overline z^{j}}m) \,, \hspace{40pt}
\mathcal Q^2 = \frac{1}{2} \hspace{1pt}\mathcal Q^T \mathcal M \hspace{1pt}\mathcal Q\,,
\end{equation}
where $\mathcal Q$ denotes the vector
$\mathcal Q = (m_I,m_a,n^I,n^a)$,
$\mathcal M$ is the positive-definite matrix similar to the one
defined in \eqref{matrix_m} and
$G^{i\overline j}$ is the inverse of the K\"ahler metric
\eqref{metric_k}.

\end{itemize}

\subsubsection*{Verifying the conjectures}

We now discuss how these conjectures are satisfied in the orientifold setting introduced in the previous section:
\begin{itemize}

\item For D3-branes wrapping odd three-cycles $\Gamma_3 \in H_{3-}(\mathcal X)$
we recall from  \eqref{d3_odd} that their $U(1)$ charges
$\mathfrak q=(m_a,n^a)$
are vanishing.
These particles do not provide the required charged particle
for the weak gravity conjecture \eqref{eq:eWGC}, but
one can check that they
verify the scalar weak gravity conjecture  \eqref{conjecture_wg}
without $U(1)$ gauge interactions \cite{Palti:2017elp}.

\item D3-branes wrapping even three-cycles $\Gamma_3 \in H_{3+}(\mathcal X)$
are massless and their charges $\mathfrak q$ are given by the wrapping numbers
$(m_a,n^a)$.
The electric weak gravity conjecture \eqref{eq:eWGC} is therefore verified. Furthermore, using \eqref{d3_even} we find that
\eq{
  \frac{1}{2}\hspace{1pt} \binom{m}{n}^T \mathcal M\hspace{1pt} \binom{m}{n} \geq 0 \,,
}
which is satisfied since the matrix $\mathcal M$ is positive definite.

\end{itemize}
We therefore conclude that the electric weak gravity conjecture
\eqref{eq:actionWGC}
and  weak gravity conjecture with scalar fields \eqref{conjecture_wg}
are trivially satisfied.

\subsubsection*{Completeness conjecture and tower versions}

The statement of the completeness conjecture is that a gravity theory with a gauge symmetry must have states of all possible charges under that gauge symmetry \cite{Polchinski:2003bq}.
In our case this conjecture is satisfied by D3-branes wrapping orientifold-even cycles $\Gamma_3\in H_{3+}(\mathcal X)$ with wrapping numbers $(m_a,n^a)$.
However, in general these states are not stable against decay to the elementary ones \eqref{states_elem}
and hence the completeness conjecture is only satisfied
as long as stability is not required.
The completeness conjecture  motivates the tower versions of the weak gravity conjecture \cite{Heidenreich:2015nta,Heidenreich:2016aqi,Andriolo:2018lvp}, which suggests that for the D3-brane particles discussed here the tower versions are satisfied only if stability of the states is relaxed.

Furthermore,
in \cite{Palti:2019pca} it is argued that avoidance of generalized global symmetries for an $U(1)$ gauge theory coupled to gravity requires at least one single charged state. Remarkably, in \cite{Gaiotto:2014kfa} it is claimed that an extension of the previous argument to discrete generalized global symmetries requires all possible charges in order to break any possible discrete symmetry. It would be interesting to explore the compatibility between our results concerning the completeness conjecture and \cite{Gaiotto:2014kfa}.

\subsubsection*{Summary and remark}

We now want to briefly summarize our findings
regarding the
weak gravity conjecture and make the following remark:
\begin{itemize}

\item We have shown that the weak gravity conjectures
for particles are verified
in type IIB orientifold compactifications
with O3- and O7-planes
for D3-branes wrapping three-cycles.
However, the tower versions  cannot be claimed to be verified as long as stability is required.

\item Analogously to type IIB orientifolds with O3-/O7-planes case studied here, the same results are obtained for type IIB orientifolds with O5-/O9-planes and for type IIA orientifolds.

\item In \cite{Font:2019cxq} it was shown that
in the orientifold
setting
BPS D5-branes wrapping three-cycles  verify the weak gravity conjecture as well. These are however
extended objects and not particles, and they
are charged under a different gauge symmetry.

\end{itemize}

\subsection{Swampland distance conjecture}

We next consider the swampland distance conjecture
for type IIB orientifolds with O3-/O7-planes
introduced above.

\subsubsection*{Recalling the conjecture}

The swampland distance conjecture
has been formulated in \cite{Ooguri:2006in}, and
has been
refined in \cite{Klaewer:2016kiy}. The refined version reads as follows:
\begin{itemize}

\item[] Consider a theory coupled to gravity with a moduli space $\mathcal M_{\rm mod}$ parametrized
by the expectation values of some fields without potential. Let the geodesic distance between any two
points $P,Q \in \mathcal{M}_{\rm mod}$ be denoted $d(P, Q)$.
If $d(P,Q) \gtrsim M_{\rm P}$, then there exists an infinite tower of states with mass scale $m$ such that
\begin{equation}
m(Q)<m(P)\,e^{-\mu\frac{d(P,Q)}{M_{\rm P}}}\,,
\label{eq:RSDC}
\end{equation}
where $\mu$ is some positive constant of order one.
This statement holds even for fields with a potential, where the moduli space is replaced with the field space in the effective theory.

\end{itemize}
We now want to verify this conjecture for the setting of the previous section. In particular, we
are starting from a generic point in complex-structure moduli space  and approach a large complex-structure point.
The results obtained in \cite{Grimm:2018ohb} for the $\mathcal N=2$ theory suggest that also
in our $\mathcal N=1$ orientifold setting D3-branes wrapping three-cycles give rise to the
infinite tower of states.
\begin{itemize}

\item We have argued that the mass of D3-branes wrapping even three-cycles $\Gamma_3 \in H_{3+}(\mathcal X)$
vanishes and hence they do not play a role for the swampland distance conjecture.

\item For D3-branes wrapping odd three-cycles $\Gamma_3 \in H_{3-}(\mathcal X)$
the $U(1)$ charges are vanishing but they are massive (cf.~equation \eqref{d3_odd}).
These states are therefore of interests for
the swampland distance conjecture.

\end{itemize}

\subsubsection*{Geodesic distance}

Let us consider a generic point in complex-structure moduli
space for which the one-loop and non-perturbative corrections to the prepotential
\eqref{prepotential_full} can be ignored.
The K\"ahler metric is computed via \eqref{metric_k}, and the geodesic equation for
such K\"ahler geometries reads in general
\eq{
  \label{geodesic_001}
  0 = \ddot z^i + \Gamma^i_{jk} \dot z^j \dot z^k\,,
  \hspace{50pt}
  \Gamma^i_{jk}  = G^{i\overline m} \partial_j G_{k\overline m} \,,
}
where a dot indicates a derivative with respect to the parametrization $t$ of the geodesic.
The geodesic distance is defined as
\eq{
  d(P,Q) = \left\lvert\int_{t_1}^{t_2} dt \sqrt{2\hspace{1pt}  \dot z^i\, G_{i\overline j}\, \dot{\overline{z}}{}^{\overline j}} \right\rvert
  \,,
  \hspace{50pt}
  \arraycolsep2pt
  \begin{array}{lcl}
  z^i(t_1) &=& P \in \mathcal{M}_{\rm mod}\,,
  \\[4pt]
  z^i(t_2) &=& Q \in \mathcal{M}_{\rm mod}\,.
  \end{array}
}
For simplicity we now restrict ourselves to a situation
with one complex-structure modulus, that is $h^{2,1}_-=1$.
We use the notation $z^1\equiv z=u+i\hspace{1pt} v$, and
the moduli space is a  hyperbolic space with metric
\eq{
  G_{1\overline 1} = \frac{3}{4}\hspace{1pt}\frac{1}{v^2} \,.
}
The solutions to the geodesic equation \eqref{geodesic_001}
are well known, and correspond to
lines with constant $u$ and to circles intersecting $v=0$ at
a right angle
\eq{
  \label{geos_004}
  z_{(1)} = \alpha + i\hspace{1pt} \beta \hspace{1pt} e^{ t}
  \,,
  \hspace{50pt}
  z_{(2)} = \alpha + \frac{\beta}{\cosh(t)}\hspace{1pt}
  \bigl[ \sinh( t) + i \bigr]\,,
}
where $\alpha,\beta={\rm const}$ and $\beta>0$.
The geodesic distance for these two cases is computed as follows
\eq{
\label{geodist}
  d_{(1)}(P,Q) &
  = \sqrt{\frac{3}{2}}\,\lvert t_Q-t_P\rvert
  =
  \sqrt{\frac{3}{2}} \left\lvert \log \frac{v_Q}{v_P} \right\rvert
  \,,
  \\
  d_{(2)}(P,Q) &= \sqrt{\frac{3}{2}}\,\lvert t_Q-t_P\rvert\,.
}

\subsubsection*{Verifying the conjecture}

As mentioned above, motivated by the $\mathcal N=2$
results we expect that  D3-branes wrapping
orientifold-odd three-cycles will provide the tower
of
states which becomes exponentially light.
In our example with $h^{2,1}_-=1$ we see that
D3-branes with wrapping numbers $n^0\neq0$ or $n^1\neq0$
do not satisfy the swampland distance conjecture \eqref{eq:RSDC}
in the large complex-structure limit $v\to\infty$;
they are expected to provide the required states
in the small complex-structure limit.
We focus here on the large complex-structure limit and D3-branes with wrapping numbers $m_0$ and $m_1$:
\begin{itemize}

\item We first consider D3-branes satisfying the
calibration condition \eqref{calibration_001}.
In this case the mass is given by
\eq{
  m(z)= \frac{1}{\sqrt{8\hspace{1pt} d_{111}v^3}}\,
  \mbox{Re}\left[ e^{i\hat\theta} \bigl(
  m_0 + m_1 z + n^0 d_{111} z^3 - 3\hspace{1pt} n^1 d_{111} z^2 \bigr) \right],
}
with $d_{111}$ the triple intersection number
introduced in \eqref{prepotential_full} and where we defined
$\hat\theta = \theta + \arg( X^0)$.
If we approach the large complex-structure limit
via the first geodesic in \eqref{geos_004},
it turns out that there
are only two choices for $\hat\theta$ compatible
with the calibration condition. The tower satisfying
the swampland distance conjecture
together with the constant $\mu$
are the following
\eq{
\arraycolsep2pt
\begin{array}{@{}lcl@{\hspace{30pt}}lcl@{\hspace{15pt}}lcl@{\hspace{15pt}}lcl@{\hspace{30pt}}lcl@{}}
\hat\theta & = & 0\,, & m_0 & > & 0\,, & m_1 & = & 0\,,
& n^a&=&0 \,,
& \mu &=& \sqrt{3/2}\,,
\\[4pt]
\hat\theta & = & \pi/2\,, & m_0 & = & 0\,, & m_1 & > & 0\,,
& n^a&=&0 \,,
& \mu &=& \sqrt{1/6}\,.
\end{array}
}

\item Next, we relax the calibration condition and
consider states satisfying the equality in
\eqref{eq:ineqBBS}.
These are the states inherited from the
$\mathcal N=2$ theory, and their mass  is given by
\eq{
  m(z) = \frac{1}{\sqrt{8\hspace{1pt} d_{111}v^3}}\,
  \Bigl|
  m_0 + m_1 z + n^0 d_{111}z^3
  -3\hspace{1pt} n^1 d_{111}z^2 \Bigr|\,.
  \label{eq:mag}
}
Approaching the large
complex-structure limit again via
first geodesic in \eqref{geos_004}, we see
that tower of states satisfying
the swampland distance conjecture are given by
\eq{
\arraycolsep2pt
\begin{array}{@{}lcl@{\hspace{30pt}}lcl@{\hspace{15pt}}lcl@{\hspace{15pt}}lcl@{\hspace{30pt}}lcl@{}}
\hphantom{\hat\theta} & \hphantom{=} & \hphantom{\pi/2\,,} & m_0 & \in & \mathbb Z\,, & m_1 & \in & \mathbb Z\,,
& n^a&=&0 \,,
& \mu &=& \sqrt{1/6}\,.
\end{array}
}

\item We also want to consider the second
geodesic in \eqref{geos_004}, for which  the
large complex-structure limit is
characterized by $\beta\ggg 1$ and $t\to 0$.
For this geodesic we do not find any
tower of D3-brane states satisfying the
swampland distance conjecture.
However, since this path is along the boundary of
the complex-structure moduli
space it is not clear whether the
conjecture applies. It would be interesting to
study this point further.

\end{itemize}
To summarize, along the path $u=\textrm{const.}$ and
$v\to\infty$ we have verified  the swampland distance conjecture for D3-particles in type IIB orientifold
compactifications, however, the tower of
states is in general not stable.
Furthermore, we were not able to verify the
swampland distance conjecture for a path
along the boundary of complex-structure moduli space.

\subsubsection*{Relation between swampland distance
and weak gravity conjectures}

For $\mathcal N=2$ theories originating from type IIB
Calabi-Yau compactifications it was found
in \cite{Grimm:2018ohb}
that the swampland distance as well as the
weak gravity conjecture are verified by BPS D3-branes wrapping special Lagrangian three-cycles.
However, for $\mathcal N=1$ theories obtained via
an orientifold projection we have noted the $h^{2,1}$  vector multiplets in $\mathcal N=2$
are projected to $h^{2,1}_-$
chiral and $h^{2,1}_+$  vector multiplets in
$\mathcal N=1$ (c.f.~equation \eqref{multiplets_split}). In particular,
in the orientifold theory both multiplets are independent
of each other, and there exist for instance orientifolds
with $h^{2,1}_+=0$.
Thus, D3-brane particles which are needed for the swampland distance conjecture are uncharged and trivially do not satisfy the electric weak gravity conjecture \eqref{eq:eWGC} --- and charged D3-brane particles satisfy the weak gravity conjecture but are not needed for the swampland distance conjecture.
Thus, the relation between the weak gravity and
swampland distance conjectures
(and emergence to be discussed below)
is determined by the bulk supergravity spectrum.

This observation extends to similar cases for which D-branes couple to a bulk spectrum in $\mathcal N=2$
which splits under the orientifold projection into different $\mathcal N=1$ multiplets. For example, in K\"ahler moduli
space the same happens for D-branes wrapping two-cycles (e.g.~the D-strings studied in \cite{Font:2019cxq}) coupling to both $J$ and $C_{2}$. It is also worth mentioning that
similar to the complex-structure moduli, also the K\"ahler twisted sector of the examples in \cite{Lust:2006zh} contains the $h_{-}^{1,1}$ cycles, so we observe an analogy with respect to the situation studied in this work.

\subsection{Emergence proposal}
\label{emergencesect}

In this section we discuss the
emergence proposal for D3-branes wrapping
three-cycles in
type IIB orientifold compactifications
with orientifold three- and seven-planes.

\subsubsection*{Recalling the proposal}

The emergence proposal has been formulated in
\cite{Grimm:2018ohb,Palti:2019pca}, which
we recall as follows:
\begin{itemize}

\item[] The dynamics (kinetic terms) for all fields are emergent in the infrared by
integrating out towers of states down from an ultraviolet scale $\Lambda_{\rm UV}
$ which is
below the Planck scale.

\end{itemize}
At a practical level this means that at an UV scale $\Lambda_{\rm UV}$, the renormalization group flow has a boundary condition on all  fields forcing them to have vanishing kinetic terms.
Let us make the following remarks concerning the emergence proposal:
\begin{itemize}

\item For towers of states with equidistant mass and charge
separation and without taking care of higher-loop corrections, it has been argued in \cite{Palti:2019pca}
that imposing emergence of gravity
one obtains
the species scale  $\Lambda_{\rm s}$
\cite{Dvali:2007hz} as the UV scale.

\item Imposing emergence of a gauge field and a
scalar field  (to one-loop order) one
recovers the magnetic weak gravity and the swampland
distance conjecture, respectively.
In \cite{Grimm:2018ohb} this mechanism has been
discussed for type IIB Calabi-Yau compactifications
with towers of states given by D3-branes wrapping
special Lagrangian three-cycles.

\item For orientifold compactifications with $\mathcal N=1$
supersymmetry in four dimensions we expect a modified picture. Indeed, the non-renormalization theorem for $\mathcal{N}=2$ changes in the case of $\mathcal{N}=1$ orientifolds as the K\"ahler potential $K_{\rm cs}$ receives loop corrections in terms of Eisenstein series
 \cite{Haack:2017vko}.
These corrections are however subleading and expected to be irrelevant as we approach the large complex-structure limit. Besides, the gauge kinetic functions remain one-loop exact.

\end{itemize}

\subsubsection*{Emergence for the orientifold-odd
third homology}

We now analyze the emergence proposal for the
orientifold-odd third cohomology.
As discussed above, D3-branes wrapping
cycles $\Gamma_3\in H_{3-}(\mathcal X)$ are massive but unstable.
Integrating out these states gives rise to logarithmic
corrections to the complex-structure moduli-space metric
of the schematic form
\eq{
  \label{running_1}
  G_{i\overline j} \bigr\rvert_{\rm IR}
  = G_{i\overline j} \bigr\rvert_{\rm UV}
  + c_- \sum_{\alpha} \bigl(\partial_{z^i} m^{(\alpha)}\bigr)
  \bigl(\partial_{\overline z^j} m^{(\alpha)}\bigr) \log\frac{\Lambda_{\rm UV}}{m^{(\alpha)}} \,,
}
where $c_-$ is a normalization constant and the sum runs over all
D3-brane states with mass below the cutoff scale $\Lambda_{\rm UV}$.
Following the argumentation of \cite{Grimm:2018ohb,Palti:2019pca}
for the emergence proposal
in the $\mathcal N=2$ setting,
the metric $G_{i\overline j}\rvert_{\rm UV}$ in the UV vanishes while
the sum over logarithmic corrections generates the
metric $G_{i\overline j}\rvert_{\rm IR}$ in the IR.
It is beyond the scope of this work to check \eqref{running_1}
explicitly for our setting, but we would like to
make the following comments:
\begin{itemize}

\item For the orientifold setting studied in this work
we have argued that the tower of D3-brane states is in general unstable. In order to verify the emergence proposal
we therefore have to integrate-out (infinite) unstable states,
which are however expected to become asymptotically-stable in the
large complex-structure limit.

\item In \cite{Font:2019cxq}
it has been proposed that also four-dimensional domain
walls contribute to the running of the moduli-space metric. These domain walls are given by
BPS D5-branes wrapping three-cycles
in the compact space, but to our knowledge it is not known how to integrate out extended objects at the quantitative level.
This ambiguity is partially reflected in the unspecified
constant $c_-$ in \eqref{running_1}.

\item It is curious to note that
in the $\mathcal N=1$ setting we have in
general all-order loop corrections to the K\"ahler potential
but also that the D3-brane particles being integrated out are
not stable.

\end{itemize}
We believe these questions deserve further
investigation in the future.

\subsubsection*{Emergence for the orientifold-even
third homology}

We now consider D3-branes wrapping orientifold-even
three-cycles $\Gamma_3\in H_{3+}(\mathcal X)$
in the compact space. These states are
massless but are charged under the closed-string
$U(1)$ gauge fields $U^a$,
and therefore contribute to one-loop
corrections to the gauge kinetic function.
In particular, in field theory we have
\eq{
  \label{running_2}
  \mbox{Re}\hspace{1pt} f^{(\rm f)}_{ab}\hspace{1pt} \bigr\rvert_{\rm IR}
  &=
  \mbox{Re}\hspace{1pt} f^{(\rm f)}_{ab}\hspace{1pt} \bigr\rvert_{\rm UV}
  + c_+ \lim_{m^{(\alpha)}\to0}
  \sum_{\alpha} \mathfrak q^{(\alpha)}_a
  \mathfrak q^{(\alpha)}_b \log\frac{\Lambda_{\rm UV}}{m^{(\alpha)}} \,,
}
where the sum is over all D3-brane particles
labelled by $\alpha$,
$\mathfrak q^{(\alpha)}_a$ denote their electric
charges and $m^{(\alpha)}$ denote their masses which vanish at the orientifold locus.
The constant $c_+$ is a normalization constant,
and the superscript indicates
that this is a field-theory result.
As expected,
we obtain logarithmic divergences  due to massless particles running in the loop.\footnote{There is an ambiguity in performing
the sum over all D3-brane particles with mass below $\Lambda_{\rm UV}$ and taking the
limit $m^{(\alpha)}\to 0$
in \eqref{running_2}. When first summing
and then taking the limit, one
obtains a polynomial divergence.}

Let us now turn  to the string-theory computation.
Using the relation \eqref{period_m_001} and the explicit form
of the prepotential \eqref{prepotential_full},
we find at the orientifold locus $X^a=0$ (without imposing $F_a=0$)
\eq{
  \label{lukas}
  \mbox{Re}\hspace{1pt} f^{({\rm s})}_{ab} = \mbox{Im}\hspace{1pt} F_{ab}
  = 6\hspace{1pt} d_{abi} v^i + (2\pi)^2 \sum_k k_a k_b \hspace{1pt} n_k \hspace{1pt}
  \mbox{Re} \log\left( 1 - e^{2\pi i k_i z^i}
  \right).
}
Here we used again $v^i = \mbox{Im}\hspace{1pt} z^i$
and the superscript indicates that this is
the (effective) string-theory result.
Following now the philosophy of the emergence proposal \cite{Grimm:2018ohb,Palti:2019pca},
the gauge-kinetic function should vanish in
the ultraviolet and the expression in
the infrared is generated by loop corrections.
In the present situation we argue as follows:
\begin{itemize}

\item The gauge-kinetic function in the infrared
is given by the expression \eqref{lukas}.
Let us then recall our
discussion from
page~\pageref{page_or_sol}
and consider the solution
\eqref{or_sol_2} to the orientifold condition $F_a=0$. Reinstalling the $X^a$-dependence
we have
\eq{
  \label{lll}
  \mbox{Re}\hspace{1pt} f^{({\rm s})}_{ab}
  = 6\hspace{1pt} d_{abi} v^i + (2\pi)^2
  \lim_{X^a\to 0}\sum_k k_a k_b \hspace{1pt} n_k \hspace{1pt}
  \mbox{Re} \log\left( - 2\pi i\hspace{1pt} k_a X^a/X^0 \right) .
}
Recalling furthermore our results for the masses from page~\pageref{page_masses_d3} and performing a similar analysis for
D3-branes wrapping orientifold-even cycles, we find for electri\-cally-charged particles that
$m=\lim_{X^a\to 0}e^{K_{\rm cs}/2} | m_a X^a |$
(in units of $M_{\rm Pl}$) with $m_{a}$ given by \eqref{states_elem}.
Using this expression in \eqref{lll},
we obtain up to prefactors and regular terms
\eq{
  \label{das_boot}
  \mbox{Re}\hspace{1pt} f_{ab}^{({\rm s})}
  \sim
  \lim_{m^{(\alpha)}\to0}
  \sum_{\alpha} k^{(\alpha)}_a
  k^{(\alpha)}_b
  \log \frac{M_{\rm s}}{m^{(\alpha)}}\,,
}
where $M_{\rm s}$ denotes the string scale
and where we relabeled the vectors $k$ appearing
in the sum by $\alpha$.
This expression has the same form
as the field-theoretical one-loop correction
shown in \eqref{running_2}, and thus
it is feasible that the emergence proposal is
verified.

\item The above-mentioned string-theory result
for the gauge-kinetic function is not complete.
Indeed, the results of \cite{Strominger:1995cz}
imply that \eqref{lukas} receives corrections in
the ultraviolet from D3-branes wrapping once around orientifold-even cycles.
Properly taking into account these states
cure the logarithmic divergence
in the Calabi-Yau moduli space, and hence
the gauge-kinetic functions
\eqref{lukas} and \eqref{lll} are expected to be
finite in a quantum-gravity theory.
In particular, in the infrared we expect
from string theory a behavior
of the form
\eq{
\label{ffull}
\mbox{Re}\hspace{1pt} f^{({\rm full})}_{ab}\hspace{1pt} \bigr\rvert_{\rm IR}
= 6\hspace{1pt} d_{abi} v^i + \mbox{finite}\,,
}
with the superscript indicating the full expression.

\end{itemize}
To summarize, we have argued that the
emergence proposal for D3-branes wrapping orientifold-even three-cycles is feasible to
be verified,
though we have presented here only qualitative analysis and a more thorough check including numerical factors and regular terms would be necessary.

\subsubsection*{Remarks and open questions}

Let us make the following remarks
concerning our discussion of
emergence in the orientifold-even sector:
\begin{itemize}

\item In our analysis we have encountered
a difference between the field-theory and
the string-theory computation.
In particular, the field-theory
expression  \eqref{running_2} for
the gauge-kinetic function is logarithmically
divergent whereas the full string-theory
expression \eqref{ffull}
is expected to be finite.

\item The gauge-kinetic function
\eqref{ffull} is the expression
expected from string theory
once the effect of D3-branes wrapping orientifold-even cycles on the moduli-space
geometry has been taken into account.
For the emergence proposal this gauge coupling
in the infrared should be obtained entirely
from loop-corrections with charged particles
running in the loop, however,
in our case these charged particles are massless and do not couple to the complex-structure moduli.
It is therefore not clear to us how the $v^i$
as well as $d_{abi}$ dependence in \eqref{ffull} can be obtained.
\begin{itemize}

\item A potential answer to this question is that there exist particles which couple simultaneously to the $U(1)$ gauge fields and to the complex-structure moduli, and where the coupling depends on $d_{abi}$, such that generate the linearly divergent term when taking into account their effect in \eqref{running_2}. However, there are no other known states with this property.

\item Another possibility is that the triple intersection numbers $d_{abi}$ vanish. This appears to be a too-strong requirement, since in T-dual settings these can be non-vanishing.

\item Since D3-branes
wrapping orientifold-even three-cycles
do not preserve the bulk supersymmetry (see
our discussion on page~\pageref{page_susy}),
the gauge-kinetic function may
receive higher-loop corrections which
can generate a term linear in $v^i$.

\end{itemize}

\item We also note that when taking the large complex-structure limit
in \eqref{ffull}, the gauge symmetry becomes global.
Although there exists an obstruction against reaching the limit $v^i\to \infty$ due to
towers of orientifold-odd D3-branes, it is unexpected to find a global gauge
symmetry associated with integrating out states
uncharged under it.
In particular, this behavior is usually associated with integrating out a tower of states which becomes massless as in \eqref{eq:RSDC} and which is charged under the gauge symmetry. However, in our setting we do not realize a possible tower of states verifying both properties.

\end{itemize}
We leave open these questions here
and refer for a more detailed description
and further instructive attempts to solve them
to section~6 of \cite{martin:2019}.

\section{Summary and conclusions}
\label{sect_conc}

In this paper we have studied swampland
conjectures for type IIB orientifolds with
O3- and O7-planes. We have allowed
for orientifold projections with
$h^{2,1}_+\neq 0$, which leads to
closed-string $U(1)$ gauge fields in
four dimensions.
The weak gravity conjecture, the swampland
distance conjecture and emergence proposal
have been investigated in the context
of the $\mathcal N=2$ parent theory
in \cite{Grimm:2018ohb}, and
here we were interested in the question
\textit{What happens to the $\mathcal N=2$
analysis when we perform
an orientifold projection?}

\subsubsection*{Summary}

Let us summarize the main results
of our analysis:
\begin{itemize}

\item The relevant objects for the
above-mentioned swampland
conjectures in our setting are D3-branes
wrapping three-cycles in the compact space.
In the $\mathcal N=2$ theory these
couple to vector multiplets, and they give rise
to four-dimensional particles charged under
$U(1)$ gauge fields and with mass depending
on the complex-structure moduli.
In the orientifold theory the
$\mathcal N=2$ vector multiplets split into
vector and chiral multiplets of $\mathcal N=1$
supergravity
as illustrated in \eqref{multiplets_split}.
Correspondingly, D3-branes can be separated
into massive-uncharged (orientifold-odd) and massless-charged (orientifold-even)
particles in four dimensions.
While for $\mathcal N=2$ these states can be
BPS and therefore can be stable, for the $\mathcal N=1$
theory they are in general unstable
and non-supersymmetric. This suggests
that the $\mathcal N=1$ swampland conjectures
studied in this paper are satisfied only for
in general
unstable states.

\item We have illustrated that
the weak gravity conjecture
\cite{ArkaniHamed:2006dz}  and the weak gravity
conjecture with scalar fields
\cite{Palti:2017elp} are trivially satisfied
in the $\mathcal N=1$ setting.
This is true both for D3-branes wrapping orientifold-odd and
orientifold-even three-cycles,
however, the tower versions can only be satisfied
if the stability requirement is relaxed.

\item We have verified the swampland distance
conjecture \cite{Ooguri:2006in,Klaewer:2016kiy}
for D3-branes wrapping orientifold-odd
three-cycles in the Calabi-Yau three-fold.
For the case $h^{2,1}_-=1$ we have studied two
types of geodesics, where one geodesic
along the boundary of the complex-structure moduli
space appears to violate the conjecture.
We noted furthermore that
the massless-charged D3-brane particles do not
contribute to the swampland distance conjecture,
and that the tower of states
is only asymptotically stable.

\item For the emergence proposal \cite{Grimm:2018ohb,Palti:2019pca}
we have seen that integrating out
D3-branes wrapping
orientifold-odd three-cycles gives
rise to the correct behavior of the
K\"ahler metric for the complex-structure moduli.
The analysis in the orientifold-even sector
was more ambiguous, but we argued that
D3-branes wrapping (collapsing) three-cycles
can re-produce the leading divergency
in the gauge-kinetic function for the closed-string
$U(1)$ gauge fields. However,
when properly taking into account
the effect of such D3-branes on the moduli-space
geometry it is expected that this divergence
is removed.
There is furthermore an open question of how
the leading regular term in
the gauge-kinetic function
can be obtained from loop corrections,
and we briefly discussed possible solutions.

\end{itemize}

\subsubsection*{Open questions and future directions}

We  comment on open questions and future
research directions:
\begin{itemize}

\item The closed-string
gauge theories originating from
the orientifold-even sector
have been studied mostly from
a supergravity point of view
and require a better understanding
within string theory.
More concretely, the implications
of the orientifold locus
$X^a=0$, $F_a=0$ on the world-sheet
instanton corrections
(c.f.~page~\pageref{page_or_loc}) need
to be clarified,
the properties of D3-branes wrapping
three-cycles $\Gamma_3 \in H_{3+}(\mathcal X)$
deserved to be  studied further, and
the emergence proposal
for the gauge theories should be made
more explicit.
To do so a concrete example would be helpful,
for which the results in \cite{Lust:2006zh}
provide
a good starting point.

\item While in the $\mathcal N=2$ setting
D3-branes wrapping three-cycles in
the compact space can be BPS, this property
is lost after orientifolding. More concretely, the corresponding states
in the four-dimensional theory no longer
preserve supersymmetry
and we expect corrections to
the mass formula for orientifold-odd
D3-branes shown in \eqref{d3_odd},
associated with their instability and with
backreaction effects onto the geometry.
We have argued that these effects should be subleading as we approach the infinite-distance limit and have disregarded them, however, such corrections should be  computed explicitly.

This is in line with results obtained in \cite{Blumenhagen:2019vgj}, where logarithmic
quantum
corrections to various swampland conjectures -- including the de-Sitter swampland conjecture -- have been discussed.
At the same time, the authors of  \cite{Ooguri:2018wrx} have connected the
de-Sitter conjecture to the  swampland distance and weak gravity conjectures.
If these connections survive in the orientifold setting, it would be interesting to see if through them
the work of \cite{Blumenhagen:2019vgj}
can shine light on the concrete form of possible modifications to the mass formula \eqref{d3_odd}, to the swampland distance and to  weak gravity conjectures for our setting.

\item In this work we focused on type IIB orientifolds with O3- and O7-planes.
It would be interesting to extend our discussion to type IIA orientifolds where a similar splitting of the $\mathcal N=2$ vector multiplet occurs \cite{Grimm:2004ua}. From mirror symmetry we expect that the mirror towers/D-branes satisfy a similar behavior, which for the $\mathcal{N}=2$ case was shown in \cite{Corvilain:2018lgw}. Besides, the E2-instantons analyzed in \cite{vittmann:2019} have properties similar to the case we studied but in the complex-structure moduli space of type IIA.
Furthermore, in the work of \cite{Font:2019cxq} it would be interesting to explore the role of the uncharged towers of extended objects.

\item Many studies of the swampland
conjectures are based on $\mathcal{N}\geq2$
supergravity theories (see \cite{DallAgata:2020ino}
for
recent work with extended supersymmetry).
However, in order to make contact with
phenomenology, theories with $\mathcal{N}=1$
supersymmetry are more suitable.
What we find in our work is that
many of the connections between the swampland conjectures and the emergence proposal are
modified for $\mathcal{N}=1$, and therefore
further studies of these connections
and their implications for phenomenology
would be desirable.

\end{itemize}

\vskip2em
\subsubsection*{Acknowledgments}

We would like to thank
R.~Blumenhagen,
L.~Martucci and
E.~Palti for very helpful discussions
and we thank D.~L\"ust for support.
EP thanks
K.~Schalm
for hospitality
and
L.~Plauschinn
for enlightening discussions.
MER is grateful to H.~Erbin for suggestions on literature concerning tachyon condensation in string field theory \cite{Sen:1999nx} and non-BPS stability \cite{Sen:1999mg} as well as to H.~\'Asmundsson, D.~Bockisch, P.~Fragkos, D.P.~Lichtig, A.~Makridou, I.~Mayer, S.P.~Mazloumi and J.D.~Sim\~ao for patient and useful discussions and finally to his family and friends for unconditional support along the period of elaboration of this work.

\clearpage
\nocite{*}

redpajama_set_name: RedPajamaArXiv


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There's a pink sign announcing a proposed Wendy's fast food restaurant next to the Spring Mills ROCS (across from Burger King). This proposal is being discussed at the next Planning Commission meeting to be held on Thursday, June 28, 2018.
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I haven't heard anything more about Wendy's.
I would also like to see Spring Mills/Falling Waters expand sit down restaurant options. I could see IHOP, Cracker Barrel or Denny's.
I could also see a fast-casual option like Chipotle or Starbucks on the horizon (Starbucks growing in the EP with new drive through locations in Martinsburg, Charles Town).
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text:
The role of fan engagement in diversifying revenue streams
A focus on authenticity to drive motivation
Highlights from Sports Pro Live Discussion Panel
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Recently, Monterosa CEO Tom McDonnell spoke with Thomas Alomes of Sports Tech World Series and Fredda Rodriguez of CONCACAF at SPLive about the role of fan engagement in diversifying revenue streams. The conversation spanned everything from driving revenue with fan engagement to the future of virtual memberships. Below are some of the key takeaways, but you can listen to the full recording for more.
Utilising fan engagement to drive revenue
When aiming to harness the revenue potential of a fanbase, attracting attention is the first challenge. The great news is, fans are already passionate, so you're starting with existing motivation. But there are so many competing forms of engagement across social media, TV, gaming and other channels, that fans often don't have your offering top of mind. To position your property as a compelling destination, the first thing you need to do is identify your fans and figure out what will compel them to show up and keep coming back.
Once that loyalty is gained, and trust is established, you can exchange that value you're providing for continued loyalty, data, and commerce. In other words, monetisation.
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How interactive experiences drive results for direct-to-consumer strategies

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Adding validation rule only if all other rules pass, or stop validating entire set of attributes on the first error in Laravel 5.7 I want to allow a user to create a folder on the local storage disk. So the form that is sent to the server quite is simple and has three attributes:

*

*new-folder-name - that is the name of the folder to be created,

*relative-path - a path to the directory inside which the new directory should be created relative to an asset root directory, and

*asset_id - the id of an asset, I need this id to get the asset's root directory.

The thing is when I validate these attributes I need to also check if the folder the user is going to create already exists. For this purpose I made a rule called FolderExists. So, before I run FolderExists, I have to be sure all other rules have passed successfully because my custom rule should accept relative-path and asset_id to be able to build the path to check against.
Here is my rules() function, I'm doing validation in custom form request:
public function rules()
{
    return [
        'asset_id' => ['bail', 'required', 'exists:assets,id'],
        'relative-path' => ['bail', 'required', 'string'],
        'new-folder-name' => ['bail', 'required', 'string', 'min:3', new FolderName, new FolderExists($this->input('asset_id'), $this->input('relative-path')]
    ];
}

So my question is:
Is it possible to add FolderExists only if all other validation rules pass?
Or maybe it's possible to stop entire validation when the validator encounters first error?
Both options should be fine here.
Thank you!

A: I have finally found the solution myself. Here is what I ended up with.
To achieve the desired result I created another validator in withValidator() method of my custom form request, this second validator will handle only the FolderExists rule and only if the previous validation fails.
public function rules()
    {
        return [
            'asset-id' => ['bail', 'required', 'integer', 'exists:assets,id'],
            'relative-path' => ['bail', 'required', 'string'],
            'new-folder-name' => ['bail', 'required', 'string', 'min:3', 'max:150', new FolderName]
        ];
    }

public function withValidator($validator)
    {
        if (!$validator->fails())
        {
            $v = Validator::make($this->input(),[
                'new-folder-name' => [new FolderExists($this->input('asset-id'), $this->input('relative-path'))]
            ]);
            $v->validate();
        }
    }

If our main validator passes, we make another validator and pass only FolderExists rule with its arguments, that have already been validated, and call validate() method. That's it.

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text:
/**
 * @author Sean sean.snow@live.com
 * @date 2015/12/27
 */

import StringBuilder from '../../lang/StringBuilder';

(() => {

    let sb = new StringBuilder();

    sb.append(123);
    console.log(sb.toString());
    console.log(sb.length())

})();

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FlexIt – the mobile-based solution that allows users to only pay for the gym time they use – announces the launch of its app, which is available in seven markets starting today. FlexIt gives consumers the freedom to choose where and when they work out, providing them with a personalized fitness experience in which there is no upfront cost and the users only pay for the time they spend in the facility. The app and platform is live in New York, New Jersey, Chicago, Washington D.C., Maryland, Virginia and Phoenix, with more than a dozen additional markets coming soon. FlexIt's line-up of partner fitness locations currently includes large national players, such as Retro Fitness and Youfit Health Clubs, as well as large regional players, such as Charter Fitness, among many others.


The market for kiosk in North America has been expanding at a robust rate in recent times, majorly due to the need for kiosks across several industries. The market players in the North American kiosk market have become accustomed to the fluctuations of the market and have been working in accordance with the varying needs of the consumers. The market for kiosk in North America displays a scenario of intense competition due to the homogenous goal of expansion held by all the market players. It is anticipated that the market vendors would elevate their quality standards and increase the utility served by the kiosks in order to attain supremacy in the market. Furthermore, the leading market players are projected to invest huge sums of money towards marketing the kiosks sold by them. This would give an upper hand to these market players because the customers are easily swayed by efficient promotion and marketing. Furthermore, the smaller market players are foreseen to form unions amongst themselves to challenge the strongholds of the larger players. Some of the key players in the North America kiosk market are Meridian Kiosks, Optical Phusion, Inc. (OPI), NCR Corporation, ZIVELO, Diebold, Inc.,Phoenix Kiosk, Olea Kiosk Inc., Kontron AG, Kiosk Information Systems, Fujitsu Ltd., Wincor Nixdorf AG, Slabb Kiosk, and RedyRef.
It is projected by Transparency Market Research (TMR) that the market for kiosk in Nortj America would reach a value of US$4.4 bn in 2024, elevating up from a value of US$2.5 bn in 2015. Furthermore, the CAGR of the North America kiosk market is expected to be 6.60% over the period between 2016 and 2024.
The demand for kiosks across the retail industry has been abundant because of the tremendous utility served by kiosk to the retail sector. Extension of inventory is an important function within the retail industry, and kiosks help in accomplishing this with palpable ease. Furthermore, bill payments and remittance of gifts can also be done through kiosks installed at the entry and exit points of retail shops. Automated retail vending machines are also a part of kiosks, which further established the relevance of kiosks in the retial sector. Besides this, the healthcare sector has also been an ardent consumer of kiosks for a range of functions. The registration of patient details in the records of hospitals is done through kiosks while the sale of medications is also carried out the same channel. Hence, the demand for kiosks in North America has been touching new heights in recent times, and is expected to keep tracing an escalating trajectory.
Despite the ascending demand graph of the market for kiosks in North America, the high costs associated with the installation and maintenance of kiosks is expected to hinder the smooth flow of the market. However, the benefits served by kiosks are tremendous, and this is expected to make up for the limitations of kiosks. The market for kiosks has done especially well in the US, majorly due to the economic stability and wellness of the healthcare sector in the country.
The review is based on TMR'S report titled "Kiosk Market (Application - Retail (Inventory Extension Kiosk, Gift Registry Kiosk, Bill Payment Kiosk, Loyalty Kiosk, Automated Retail Vending Kiosk), Healthcare (Wayfinding/Directory Kiosks, Patient Check-in/Check-out Kiosk, Hospital Information Kiosk, Human Resource Kiosk, Virtual Receptionist Kiosk, Patient/Physician Communication Portal) - North America Industry Analysis, Size, Share, Growth, Trends and Forecast 2016 – 2024".


A mechanical permit enables you to install new mechanical equipment such as heating, venting, and air conditioning (HVAC) equipment and kitchen hood exhaust systems. It does not enable you to install plumbing, sprinklers, gas lines, refrigeration, and boiler pressure vessels; these all require a separate permit. See Tip 415, Applicant Responsibilities and Plan Requirements for Mechanical Permits, for information about the types of mechanical permits and submittal requirements.
You can get a mechanical permit as part of your construction permit, or you can get it separately.
You may also need a business license if your project is in Seattle, even if your office is outside the city.
We base your permit fees on the value of construction plus an hourly review fee. We also collect an additional fire review fee for kitchen hood exhaust systems. We describe your fees in more detail in our Fee Subtitle.
For most projects, you should plan for 9 weeks from the time you apply to the time we issue your permit. We try to finish our initial review of complex projects in 4 weeks, and 2 weeks for simple projects. We often ask you to make corrections after the initial review, which triggers a second review of your corrected plans.
The time it takes to get your mechanical permit depends on how complex your project is, how many corrections of your plans you need to make, and how quickly and completely you respond.
If your project is simple (see the Tip below), we can issue you a mechanical subject-to-field-inspection permit within 24 hours.
Determine restrictions to your project. Research the codes to determine unit noise limits requirements.
Start your application. Complete the Building & Land Use Pre-Application online using the Seattle Services Portal. If you are applying for a mecahnical STFI permit, you need to upload your plans and contractor disclosure form at the time of your application.
Request a pre-submittal conference (optional). We recommend pre-submittal conferences for very complex projects, including buildings with unusual structural systems, substantial alterations, or work in environmentally critical areas or shorelines. Request a pre-application site visit online through the Seattle Services Portal. One-hour pre-submittal conference fees vary based on the type of conference you need.
Get mechanical tech support. We offer technical backup support to answer questions before you apply for a mechanical permit. This service is available on a first-come, first-served basis for walk-in customers at the Applicant Services Center.
Apply for exemptions. You may need an exemption from code requirements if your project is located in an environmentally critical area or near the shoreline. You may also ask for a code modification if you propose to use a code that Seattle hasn't yet adopted.
Coordinate with other agencies. You may need permits from other City of Seattle departments.
Prepare a complete set of drawings. Include a mechanical plan coversheet, vicinity map, site plan, and plans and elevations. For a detailed list of requirements see Tip 415, below. Also provide an equipment schedule (an example is in Tip 415) and heating and cooling load calculations where applicable. Be sure to list any exceptions you have taken.
If you are installing a commercial kitchen hood, include the Commercial Kitchen Hood Worksheet as part of your drawing set on a full-size sheet.
You need to show the dimensions from the unit to the property line on your plans. You must meet the standards in our noise code.
Include structural information when you submit your permit. You need to include calculations by a licensed structural engineer indicating the existing structure is adequate, as well as seismic calculations for unit anchorage. Include your unit seismic anchor details in your drawing set (full-size sheet), stamped by the structural engineer.
Schedule an intake appointment. You can schedule an electronic intake appointment once your screening is approved and you have completed all required preliminary application steps. You must upload all application documents by 7:00 a.m. on the day of your appointment. We may contact you that day for more information.
Pay fees. Approximately 75 percent of your permit fees are due at intake. The fees are calculated based on your project value. You must pay these fees before we will review your plans.
Request an inspection. See the mechanical inspections page for when to call us and how to schedule your inspection.


text:
About the Usability of a Photovoltaic Module to Monitor Air Pollution
Viktor Schlosser, Markus Drapalik, Gerhard Klinger
The responsivity by means of the quotient of photo-current and incident global light intensity of a solar module situated in central Vienna was analyzed during a period where an ash cloud of volcanic origin was spread over central Europe in spring 2010. A timely coincidence between anomalies of the registered responsivity and the concentration of ash particles in the air was found. However due to the lack of reliable directly observed particle concentration no correlation could be established.
Electronic Properties of Materials, Department of Meteorology and Geophysics
https://doi.org/10.1109/ICCEP.2011.6036378
Solid state physics, Materials physics
https://ucris.univie.ac.at/portal/en/publications/about-the-usability-of-a-photovoltaic-module-to-monitor-air-pollution(398e70f8-7380-4af6-bf07-e01dcee19285).html


text:
List of Cities with Paid Leave Ordinances. Will Austin Be Next?
February 15, 2018 By Jessica Miller-Merrell Leave a Comment
Now that I'm a resident of Austin, I'd like to talk about a proposed paid sick leave ordinance that is up for a vote by the Austin City Council on February 15, 2018.
The proposed ordinance mandating all private employers to pay sick leave would be a first for Texas. The ordinance requires that employers allow employees to earn one hour of sick time per 30 hours worked, capped at 64 hours, or face a $500 penalty per violation.
As a tech hub, Austin businesses are already recruiting in a highly competitive market. The ordinance will likely push employers to boost benefit packages in order to attract top talent, but also remove the employers' ability to customize what it offers in order to fall in line with the paid sick leave mandate. However, the ordinance would not usurp current sick policies in place at private employers who provide eight or more days of sick leave or paid time off.
How Mandated Paid Leave Benefits Can Benefit Austin Residents
Forcing one benefit over others isn't necessarily good for Austin's workforce or Austin's economy. While tech companies are most concerned about losing the ability to customize benefits, the ordinance would have the greatest effect on the maintenance, construction and service industries, that last group including restaurant staff and caretakers. Between 65 and 70 percent of employees in those sectors do not have access to sick leave, according to data from Work Strong Austin, a coalition of activist groups supporting the ordinance.
Last year, the Austin Independent Business Alliance surveyed more than 100 employers and found that a large majority were against the city regulating sick pay. Of the surveyed businesses that do not provide sick leave, 70 percent cited costs as the reason. This could mean a huge impact on overhead cost for employers, potentially forcing them to cut costs in other areas (like salaries or perks).
Other Cities with Mandated Paid Leave Programs
I took a look at several cities that have specific paid leave ordinances and how they are structured. At the minimum, these policies cut down on the number of employees that come to work sick and infect others. Some of them even specifically include domestic violence and stalking.
Under Seattle's Paid Sick and Safe Time ordinance, all employees working in Seattle accrue paid leave that can be used for absences due to the care of a personal or family member's health condition or critical safety reason. On September 1, 2012, the initial ordinance went into effect for all employers with more than four full-time equivalents. In December 2017, the ordinance was amended to significantly expand employer coverage and employee rights.
Beginning July 1, 2017, workers in Minneapolis accrue one hour of sick and safe time for every 30 hours worked, thanks to the city's Sick and Safe Time ordinance. Workers will accrue up to 48 hours per year, the unused portion of which can carry over to the following year, but after that, that accrual balance in following years cannot exceed 80 hours – and that includes salaried employees or other "exempt" workers.
The San Francisco Paid Sick Leave Ordinance became effective on February 5, 2007. All employers must provide paid sick leave to each employee (including temporary and part-time employees) who performs work in San Francisco.
Chicago, Ilinois
In June 2017, the Chicago City Council unanimously approved a new paid sick leave ordinance that requires every employer in the city to provide at least some paid time off to employees for sick leave purposes. The ordinance is effective as of July 1, 2017 and covers any employee who works within Chicago's city limits and works 80 or more hours within a 120-day period. Employers must provide workers the right to accrue and use up to 5 paid sick days (or 40 hours) per year, earned at a minimum rate of one hour for every 40 hours worked. Workers must be allowed to roll over up to 20 hours of unused sick leave into the subsequent year.
In November 2014, Oakland voters overwhelmingly passed Measure FF, an amendment to the Oakland Municipal Code establishing a minimum wage, requiring payment for accrued sick leave and requiring payment of service charges to hospitality workers. The measure establishes a minimum wage in the City of Oakland of $12.25 per hour, beginning on March 2, 2015. The measure also requires that employers in Oakland provide paid sick leave to their employees beginning on March 2, 2015, and requires that hospitality employers who collect service charges from customers pay all service charges to their hospitality workers.
On June 2, 2016, Los Angeles Mayor Eric Garcetti signed into law Ordinance Nos. 184319 and 184320, which create enhanced paid sick leave rights for employees working within the City of Los Angeles. Beginning on July 1, 2016, employers covered by both the California Healthy Workplaces, Healthy Families Act of 2014 and the Ordinances will need to comply with the more generous provisions of the Ordinances. As a result, employees working in the City of Los Angeles will be entitled to up to 48 hours of paid sick leave per year, nearly twice the amount as most of their non-Angelino counterparts.
The City of San Diego's Earned Sick Leave and Minimum Wage Ordinance, San Diego Municipal Code (SDMC) Chapter 3, Article 9, Division 1 became effective on July 11, 2016. It is applicable to employees who perform at least two (2) hours of work in one or more calendar weeks of the year within the geographic boundaries of San Diego. Employers must provide each employee earned sick leave. Employees must accrue no less than one (1) hour of earned sick leave for every thirty (30) hours worked within the geographic boundaries of the City; employers may cap the total accrual of sick leave at eighty (80) hours. Any unused accrued earned sick leave must be carried forward to the following benefit year.
The Tacoma Paid Leave Act took effect February 1, 2016. Employees started earning sick leave. Employees earn 1 hour of sick leave for every 40 hours worked. Employees are able to earn up to a minimum of 24 hours of paid leave each year. Employers can cap leave usage at 24 hours a year. Calendar Year is defined in the ordinance as a calendar year, a 12 month period starting on the date of the employee's hire date or a fiscal year.
New Brunswick's paid leave ordinance is particularly interesting, as it focuses on domestic abuse and violence:
On January 6, 2016, the New Brunswick Paid Sick/Safe Time Ordinance became effective. The purpose of the Ordinance is to allow employees paid time off from their job to take care of health or domestic violence issues for themselves and their family. Employees working at eligible businesses qualify for paid sick/safe time if they average at least 20 hours of work per week. Part-time workers who average between 20 and 35 hours per week can earn up to 24 hours of paid sick/safe time. Full-time workers who average 35 hours per week or more can earn up to 40 hours of paid sick/safe time. Eligible employees begin to earn sick/safe time once the Ordinance became effective. Employees can begin to use sick/safe time either 120 days after the Ordinance became effective (May 5, 2016) or 120 days after they started work if hired after the effective date.
As you can see city specific paid leave programs continue to grow in popularity, and I think given the continued growth in Austin combined with the growing employment divide tech versus service in Austin, a mandated paid leave program just might be the right step for all Austin residents. Many business owners are concerned because of the swift move by the city to move forward with the vote leaving employers with many questions and concerns about how quickly the ordinance if passed will be put into effect.
Are you in favor or opposed to Austin's mandated sick time ordinance?
Filed Under: HR, Work Tagged With: AUSTIN, mandated sick leave, paid leave, sick leave
About Jessica Miller-Merrell
Jessica Miller-Merrell, is workplace change agent and author focused on human resources and talent acquisition living in Austin, TX. Recognized by Forbes as a top 50 social media influencer. She's the founder of Workology. Follow her on Twitter, @jmillermerrell.