text:
Authorize external services in your Office Add-in
Popular online services, including Office 365, Google, Facebook, LinkedIn, SalesForce, and GitHub, let developers give users access to their accounts in other applications. This gives you the ability to include these services in your Office Add-in.
The remainder of this article is about accessing non-Microsoft services. For information about accessing Microsoft Graph (including Office 365), see Access to Microsoft Graph with SSO and Access to Microsoft Graph without SSO.
The industry standard framework for enabling web application access to an online service is OAuth 2.0. In most situations, you don't need to know the details of how the framework works to use it in your add-in. Many libraries are available that simplify the details for you.
A fundamental idea of OAuth is that an application can be a security principal unto itself, just like a user or a group, with its own identity and set of permissions. In the most typical scenarios, when the user takes an action in the Office Add-in that requires the online service, the add-in sends the service a request for a specific set of permissions to the user's account. The service then prompts the user to grant the add-in those permissions. After the permissions are granted, the service sends the add-in a small encoded access token. The add-in can use the service by including the token in all its requests to the service's APIs. But the add-in can act only within the permissions that the user granted it. The token also expires after a specified time.
Several OAuth patterns, called flows or grant types, are designed for different scenarios. The following two patterns are the most commonly implemented:
Implicit flow: Communication between the add-in and the online service is implemented with client-side JavaScript. This flow is commonly used in single-page applications (SPAs).
Authorization Code flow: Communication is server-to-server between your add-in's web application and the online service. So, it is implemented with server-side code.
The purpose of an OAuth flow is to secure the identity and authorization of the application. In the Authorization Code flow, you're provided a client secret that needs to be kept hidden. An application that has no server-side backend, such as an SPA, has no way to protect the secret, so we recommend that you use the Implicit flow in SPAs.
You should be familiar with the pros and cons of the Implicit flow and the Authorization Code flow. For more information about these two flows, see Authorization Code and Implicit.
You also have the option of using a middleman service to perform authorization and pass the access token to your add-in. For details about this scenario, see the Middleman services section later in this article.
Using the Implicit flow in Office Add-ins
The best way to find out if an online service supports the Implicit flow is to consult the service's documentation.
For information about libraries that support the Implicit flow, see the Libraries section later in this article.
Using the Authorization Code flow in Office Add-ins
Many libraries are available for implementing the Authorization Code flow in various languages and frameworks. For more information about some of these libraries, see the Libraries section later in this article.
Libraries are available for many languages and platforms, for both the Implicit flow and the Authorization Code flow. Some libraries are general purpose, while others are for specific online services.
Google: Search GitHub.com/Google for "auth" or the name of your language. Most of the relevant repos are named google-auth-library-[name of language].
Facebook: Search Facebook for Developers for "library" or "sdk".
General OAuth 2.0: A page of links to libraries for over a dozen languages is maintained by the IETF OAuth Working Group at: OAuth Code. Note that some of these libraries are for implementing an OAuth compliant service. The libraries of interest to you as a an add-in developer are called client libraries on this page because your web server is a client of the OAuth compliant service.
Middleman services
Your add-in can use a middleman service such as OAuth.io or Auth0 to perform authorization. A middleman service may either provide access tokens for popular online services or simplify the process of enabling social login for your add-in, or both. With very little code, your add-in can use either client-side script or server-side code to connect to the middleman service and it will send your add-in any required tokens for the online service. All of the authorization implementation code is in the middleman service.
We recommend that the UI for authentication/authorization in your add-in use our Dialog APIs to open a login page. See Use the Dialog APIs in an authentication flow for more information. When you open an Office dialog in this way, the dialog has a completely new and separate instance of the browser and JavaScript engine from the instance in the parent page (e.g., the add-in's task pane or FunctionFile). A token, and any other information that can be converted to a string, is passed back to the parent using an API called messageParent. The parent page can then use the token to make authorized calls to the resource. Because of this architecture, you must be careful how you use the APIs provided by a middleman service. Often the service will provide an API set in which your code creates some kind of context object which both gets a token and uses that token in making subsequent calls to the resource. Often the service has a single API method that makes the initial call and creates the context object. An object like this cannot be completely stringified, so it cannot be passed from the Office dialog to the parent page. Typically, the middleman service provides a second API set, at a lower level of abstraction, such as a REST API. This second set will have an API that gets a token from the service, and other APIs that pass the token to service when using it to get authorized access to the resource. You need to work with an API at this lower level of abstraction so that you can get the token in the Office dialog and then use messageParent to pass it to the parent page.
CORS stands for Cross Origin Resource Sharing. For information about how to use CORS inside add-ins, see Addressing same-origin policy limitations in Office Add-ins.


text:
package com.github.rodm.teamcity.internal;

import com.github.rodm.teamcity.BaseTeamCityEnvironment;
import com.github.rodm.teamcity.LocalTeamCityEnvironment;
import org.gradle.api.model.ObjectFactory;
import org.gradle.api.provider.Property;
import org.gradle.api.provider.Provider;

import javax.inject.Inject;

public class DefaultLocalTeamCityEnvironment extends BaseTeamCityEnvironment implements LocalTeamCityEnvironment {

    private final DefaultTeamCityEnvironments environments;

    private final Property<String> downloadUrl;
    private final Provider<String> installerFile;
    private final Property<String> homeDir;
    private final Property<String> javaHome;

    @Inject
    public DefaultLocalTeamCityEnvironment(String name, DefaultTeamCityEnvironments environments, ObjectFactory factory) {
        super(name, environments, factory);
        this.environments = environments;
        this.downloadUrl = factory.property(String.class).convention(defaultDownloadUrl());
        this.installerFile = factory.property(String.class).convention(defaultInstallerFile());
        this.homeDir = factory.property(String.class).convention(defaultHomeDir());
        this.javaHome = factory.property(String.class).convention(System.getProperty("java.home"));
    }

    /**
     * The download URL used to download the TeamCity distribution for this environment.
     */
    public String getDownloadUrl() {
        return gradleProperty(propertyName("downloadUrl")).orElse(downloadUrl).get();
    }

    public void setDownloadUrl(String downloadUrl) {
        this.downloadUrl.set(downloadUrl);
    }

    public Provider<String> getInstallerFile() {
        return installerFile;
    }

    /**
     * The home directory for this environment's TeamCity installation.
     */
    public String getHomeDir() {
        return getHomeDirProperty().get();
    }

    public void setHomeDir(String homeDir) {
        this.homeDir.set(homeDir);
    }

    public Provider<String> getHomeDirProperty() {
        return gradleProperty(propertyName("homeDir")).orElse(homeDir);
    }

    /**
     * The Java home directory used to start the server and agent for this environment.
     */
    public String getJavaHome() {
        return getJavaHomeProperty().get();
    }

    public void setJavaHome(String javaHome) {
        this.javaHome.set(javaHome);
    }

    public Provider<String> getJavaHomeProperty() {
        return gradleProperty(propertyName("javaHome")).orElse(javaHome);
    }

    private Provider<String> defaultDownloadUrl() {
        return environments.getBaseDownloadUrlProperty().map(baseUrl -> baseUrl + "/TeamCity-" + getVersion() + ".tar.gz");
    }

    private Provider<String> defaultInstallerFile() {
        return environments.getDownloadsDirProperty().map(dir -> dir + "/" + filename());
    }

    private String filename() {
        String url = downloadUrl.get();
        int index = url.lastIndexOf("/") + 1;
        return url.substring(index);
    }

    private Provider<String> defaultHomeDir() {
        return environments.getBaseHomeDirProperty().map(dir -> dir + "/TeamCity-" + getVersion());
    }
}

redpajama_set_name: RedPajamaGithub


4% COMMISSION EXTENDED!! CAN END AT ANY TIME! This home has design features that Wow! As you enter the large foyer you can tell you've entered a quality home with lots designer details throughout. This plan features a study or 5th BR on the main level with a full bath. The great room, dining room and kitchen all flow together seamlessly and make entertaining a breeze! The kitchen has a bar and granite counter tops, gorgeous cabinets with crown molding,and a mudroom/pantry space. The spacious owner's suite is on the 2nd floor as well as the laundry room and two BRs w/ walk in closets-hurray! and a bathroom. 3rd level has a great bonus room,large BR and full bath. A great floor for a teenager or in-laws.! If desired a screened porch can be added. Ready NOW!


text:
\section{Introduction}

At ultra-high energies, of order the Planck mass, the scattering of elementary particles is dominated by
graviton exchange. Scattering at these energies is therefore an important theoretical laboratory in which
to test fundamental ideas in quantum field theory, string theory and quantum gravity
(see refs.~\cite{'tHooft:1987rb,Muzinich:1987in,Amati:1987wq,Gross:1987kza,Gross:1987ar,Amati:1987uf,Amati:1988tn,
Amati:1990xe,Amati:1992zb,Amati:1993tb,Veneziano:2004er,Amati:2007ak,Giddings:2007bw,
Giddings:2009gj,Giddings:2011xs}).
The key technique used in the analysis is the eikonal approximation, which allows one to effectively
sum up an infinite set of ladder diagrams for exchanging an arbitrary number of gravitons.

As a scattering problem, the natural quantity to define is the
eikonal phase $\Theta(s,b)$, written in terms of the Mandelstam variable $s=4EE'$, where $E$ and $E'$ are the
energies of the particles, and the impact parameter $b$.
The expression for the eikonal amplitude in terms of the usual pair of Mandelstam variables $(s,t)$
is then obtained by a Fourier transform,
\EQ{
{\cal A}(s,t=-\vec q^{\,2})=-2is\int d^{d-2}b\,e^{i\vec b\cdot\vec q}\left[e^{i\Theta(s,b)}-1\right]\ .
\label{a1}
}
In the ultra-high energy regime, we allow the dimensionless ratio $G s/b^{d-4}$
which determines the leading order eikonal phase to be large
(recall that in $d$ spacetime dimensions, $G = 1/M_p^{d-2}$).

As shown in \cite{'tHooft:1987rb}, the eikonal approximation allows the reformulation of the two-particle
scattering problem in terms of the classical propagation of the first particle in the Aichelburg-Sexl shockwave
geometry \cite{Aichelburg:1970dh} produced by the other. The leading order phase $\Theta_{\rm cl}(s,b)$
is then given in terms of the discontinuous lightcone coordinate shift experienced by particle 1
as it passes the shockwave. For example, in four dimensions the phase shift is
$\Theta_{\rm cl} \sim - G s \log \left(b^2 \Lambda^2\right)$, for some cut-off $\Lambda$,
leading to the amplitude \cite{'tHooft:1987rb}
\EQ{
{\cal A}(s,t) = 8\pi i \,\frac{s}{t} \left(\frac{-t}{4\Lambda^2}\right)^{iGs} \frac{\Gamma(1-iGs)}{\Gamma(iGs)}
\qquad  \implies \qquad
\left|{\cal A}(s,t)\right|^2 = (8\pi)^2\, \frac{G^2 s^4}{t^2} \ .
\label{a2}
}

Moving beyond this classical picture, in an interacting QFT the propagating particle has an associated vacuum polarization
cloud, characterised by the length scale $\lambda_c \sim 1/m$ of the virtual particles in the loop. In the shockwave
background, this is subject to gravitational tidal forces, which give a new quantum contribution to the phase shift,
\EQ{
\Theta(s,b) = \Theta_{\rm cl}(s,b) + \Theta_{\rm scat}(\hat{s}) \ ,
\label{a3}
}
where, as we see later, this further shift depends only on the combination
$\hat{s} = Gs/m^2 b^{d-2}$ of the CM energy and impact parameter.

At low energies, $\Theta_{\rm scat}(\hat{s})$ is described by an effective action describing the coupling of the curvature
to the quantum fields. This coupling violates the strong equivalence principle and is known in many instances to
produce apparent causality violations in the form of superluminal propagation. In the context of gravitational shockwave
scattering, this is manifested as a Shapiro {\it time advance}. However, in order to determine
whether or not such a potential causality violation is really physical, we have to look at the high-energy limit.
This means going beyond the effective theory and determining the scattering phase $\Theta_{\rm scat}(\hat{s})$
in the full, UV complete QFT.

In a recent paper \cite{Hollowood:2015elj}, we have shown by explicit calculation of the full energy dependence
of the scattering phase, how in a renormalisable theory, QED in four dimensions,
the apparent causality violations arising from $\Theta_{\rm scat}(\hat{s})$ in the effective theory
are resolved in the UV limit. It is an interesting question, which we leave for future work, how these apparent
causality problems manifest themselves in the scattering amplitude ${\cal A}(s,t)$, how they are related to
the unitarity properties of ${\cal A}(s,t)$ and the associated partial wave amplitudes, and how they are
resolved by the $\hat{s}\rightarrow\infty$ limit in the QFT picture of propagation in the shockwave spacetime.

Here, as a prelude to such investigations, we study the IR and UV properties of the scattering phase
$\Theta_{\rm scat}(\hat{s})$ for a range of QFTs exhibiting different renormalizability properties
in order to gain a clearer understanding of the interplay of causality, unitarity and renormalizability in the
presence of the shockwave background.
This was prompted by the observation in \cite{Hollowood:2015elj} that the UV behaviour of the
scattering phase in a purely scalar, super-renormalizable analogue of QED was quite different from QED itself,
although still maintaining causality. To this end, in this paper we study the scattering problem for a class
of self-interacting $\phi^n$ scalar theories in $d$ dimensions for arbitrary $n$ and $d$,
and investigate in detail the relation of causality and renormalizability in the gravitational shockwave
background. Quite generally, the study of effective field theories in gravitational
shockwave spacetimes is a rigorous test of what constraints are placed on the form and values of the
couplings in an effective theory in order that it admits a consistent UV completion.

There is a clear parallel between this programme and the pure gravity case, where the scattering particles are
themselves gravitons. In the paper \cite{Camanho:2014apa}, the effective field theory is taken to be the
Einstein action augmented by a Gauss-Bonnet term.
As shown there, this effective theory exhibits superluminal causality violation. In this case, one resolution is that the
effective theory must be embedded in a UV complete theory containing an infinite set of higher spin states
that Reggeizes the amplitude as in string theory \cite{Camanho:2014apa,D'Appollonio:2015gpa}.
Note here the crucial r\^ole played by the introduction of the string scale $\lambda_s$, which is analogous
to the scale $\lambda_c$ in our QFT problem. Another interesting issue relevant to the Gauss-Bonnet case, is whether the causality-violating configuration of gravitational shockwaves can actually be engineered in the first place \cite{Papallo:2015rna}.

\subsection{Ultra-high energy scattering and shockwaves}

As  discussed above, ultra-high energy scattering can be viewed in the eikonal approximation in terms
of propagation in a gravitational shockwave background, as illustrated in fig.~1.
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=0.7,fill=black!20,decoration={markings,mark=at position 0.5 with {\arrow{>}}}]
\begin{scope}[xshift=15.5cm,yshift=0.4cm]
\node at (0.8,0.2) {$=$};
\end{scope}
\begin{scope}[xshift=9cm,yshift=0cm]
\begin{scope}[scale=0.9]
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (0,1.5) -- (0,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (0.5,1.5) -- (2,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (2,1.5) -- (0.5,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (2.5,1.5) -- (2.5,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (3,1.5) -- (3.5,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (5,1.5) -- (4.5,0);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (5.5,1.5) -- (5.5,0);
\draw[very thick] (-1,2.5) -- (0,1.5) -- (3.5,1.5);
\draw[very thick,densely dashed] (3.5,1.5) -- (4.5,1.5);
\draw[very thick]  (4.5,1.5) -- (5.5,1.5) -- (6.5,2.5);
\draw[very thick] (-1,-1) -- (0,0) -- (3.5,0);
\draw[very thick,densely dashed] (3.5,0) -- (4.5,0);
\draw[dashed] (3.5,0.75) -- (4.5,0.75);
\draw[very thick] (4.5,0) -- (5.5,0) -- (6.5,-1);
\end{scope}
\node at (-2,0.75) {$\Large\displaystyle\sum$};
\node at (-2,-0.2) {\footnotesize gravitons};
\end{scope}
\begin{scope}[xshift=18cm,yshift=-1.2cm,scale=0.6]
\draw[line width=2mm,color=black!20] (7,0) --  (0,7);
\draw[very thick,postaction={decorate}] (0,0) -- (3.5,3.5);
\draw[very thick,postaction={decorate}] (2.5,4.5) -- (5,7);
\draw[very thick,postaction={decorate}] (3.5,3.5) -- (2.5,4.5);
\node[rotate=45] at (1,2) {$v=0$};
\node[rotate=-45] at (6.4,1.8) {$u=0$};
\node at (6.8,7.7) {$v=\Delta v$}; \end{scope}
\end{tikzpicture}
\caption {\footnotesize  The tree level gravitational scattering of two high energy particles can be improved by
summing over ladder diagrams (including crossings) involving multiple graviton exchange.
This re-summation is equivalent to studying the classical motion, the null geodesics, of one of the particles
in the Aichelburg-Sexl shockwave produced by the other.
The scattering is then described by a Shapiro time delay, or advance, of the particle as it crosses the shockwave.}
\label{f1}
\end{center}
\end{figure}

A central role is played, therefore, by the Aichelburg-Sexl metric \cite{Aichelburg:1970dh},
\begin{equation}
ds^2 = -2 du \,dv + f(r) \delta(u) du^2 +\sum_{i=1}^{d-2} dx^i\,dx^i\ ,\qquad r^2=\sum_{i=1}^{d-2}x^ix^i\ .
\label{ba}
\end{equation}
The profile function $f(r)$ is determined by the Ricci curvature $R_{uu} = 8\pi G T_{uu}$
and depends on the nature of the matter source for the shockwave.
For the case of an ultra-high energy particle of energy $E'$, the profile function $f(r)$ is
\EQ{
f(r)=\frac{4\Gamma(\frac{d-4}2)}{\pi^{\frac{d-4}2}}\cdot\frac{GE'}{r^{d-4}}\ .
\label{bb}
}
This particle follows the trajectory $u=x^i=0$, {\it i.e.}~$r=0$.

At very high energy, i.e.~for the scalar field $E\gg m$, particle 1 then follows a null geodesic propagating
in the opposite direction to the shockwave, that is $v=0$ and impact parameter $r=b$. The fact that we
can talk about particle trajectories means that we are working in the geometric optics limit,
which requires $E\gg\sigma$, where $\sigma$ is the curvature scale expressed as a mass scale.
For the shockwave, $\sigma\sim GE'/b^{d-2}$.

Along the geodesic followed by particle 1, the null coordinate takes the form
\begin{equation}
v = \frac{1}{2} f(b) \vartheta(u) + \frac{1}{8} f'(b)^2 u \vartheta(u) \ .
\label{ab}
\end{equation}
The first term here, corresponds to a instantaneous jump in the null coordinate $v$ as the particle
passes through the shockwave wavefront at $u=0$:
\EQ{
\Delta v=\frac12f(b)=\frac{2\Gamma(\frac{d-4}2)}{\pi^{\frac{d-4}2}}\cdot\frac{GE'}{b^{d-4}}\ ,
}
In four dimensions, this is
\EQ{
(d=4):\qquad \Delta v= -2G E'\log\Big(\frac b{r_0}\Big)^2 ,
}
where $r_0 = 1/\Lambda$ is short-distance regulator.\footnote{This can be established by regularizing the
particle as a beam shockwave \cite{Ferrari:1988cc} with radius $r_0$.} In $d=4$, therefore,
the shift in the null coordinate is actually a Shapiro time advance.

Thinking of a wave packet with a narrow spread of energies implies that the eikonal phase itself
is related to the shift in the null coordinate by
\EQ{
\Delta v=\operatorname{Re}\frac{\partial\Theta}{\partial E}\ .
\label{zz1}
}
Note that, in general, the eikonal phase can have a imaginary part which is interpreted as a
modulation of the amplitide of the mode. In the shockwave case, therefore,
\EQ{
\Theta_{\rm cl}(s,b)=\frac{\Gamma(\frac{d-4}2)}{2\pi^{\frac{d-4}2}}\cdot\frac{Gs}{b^{d-4}}\ .
}

The time advance in the case $d=4$ is interesting: does this imply a breakdown of causality?
The answer turns out to be quite subtle. One way to approach it is to construct a geometry,
a ``time machine", that allows particles to propagate around a closed trajectory.
The simplest setup, first introduced in \cite{Shore:2002in} and then considered in
\cite{Adams:2006sv,Camanho:2014apa}, consists of two shockwaves that collide wth some
impact parameter $L$: see the left-hand side of fig.~\ref{f2}.

\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=0.6,fill=black!20,decoration={markings,mark=at position 0.6 with {\arrow{>}}}]
\draw[line width=2mm,color=black!20] (0,0) -- (7,7);
\draw[line width=2mm,color=black!20] (7,0) --  (0,7);
\draw[very thick,postaction={decorate}] (0,4) -- (1.5,5.5);
\draw[very thick,postaction={decorate}] (1.5,5.5) -- (5.5,1.5);
\draw[very thick,postaction={decorate}] (5.5,1.5) -- (6,6);
\draw[very thick,postaction={decorate}] (6,6) -- (1,1);
\draw[very thick,postaction={decorate}] (1,1) -- (1.4,3.2);
\node at (0.6,5.7) {$S$};
\node at (6.2,1.6) {$P$};
\node at (6.5,5.6) {$Q$};
\node at (0.3,1.2) {$R$};
\node at (3.5,2.8) {$O$};
\node[rotate=45] at (6,6.8) {$v=0$};
\node[rotate=-45] at (1,6.8) {$u=0$};
\node[opacity=0.4] at (-1,6) {shock 1};
\node[opacity=0.4] at (8.3,6) {shock 2};
\end{tikzpicture}
\begin{tikzpicture}[scale=0.6,fill=black!20,decoration={markings,mark=at position 0.6 with {\arrow{>}}}]
\draw[line width=2mm,color=black!20] (0,1) -- (3,4);
\draw[line width=2mm,color=black!20] (6.5,0.5) -- (9,3);
\draw[line width=2mm,color=black!20] (7,0) -- (0,7);
\draw[very thick,postaction={decorate}] (0,4) -- (1.5,5.5);
\draw[very thick,postaction={decorate}] (1.5,5.5) -- (5.5,1.5);
\draw[very thick,postaction={decorate}] (5.5,1.5) -- (6,6);
\node at (0.6,5.6) {$S$};
\node at (6.2,1.7) {$P$};
\node at (3,3.3) {$O$};
\node[rotate=45] at (0.8,2.6) {$v=0$};
\node[rotate=45] at (7.9,2.7) {$v=\Delta v$};
\node[rotate=-45] at (1,6.8) {$u=0$};
\node[opacity=0.4] at (-1,6) {shock 1};
\node[opacity=0.4] at (9.3,1.5) {shock 2};
\node[opacity=0.4] at (0.3,0.4) {shock 2};
\end{tikzpicture}
\caption{\footnotesize Left: the proposed time machine consisting of two shockwaves
moving in opposite directions that collide at $O$. The particle collides with the first at $S$,
experiences a shift back to $P$ which then allows it to catch up with shockwave 2 with a
jump back to $R$ in the past lightcone of $S$. Right: in the true picture, the wavefront of
shockwave 2 at the same impact parameter as the particle undergoes the same shift
$\Delta v<0$ as the particle. It is clear that the particle can, therefore never catch up
with the shockwave 2 to complete the circuit shown on the left.}
\label{f2}
\end{center}
\end{figure}

In fact, a careful analysis \cite{Shore:2002in,Hollowood:2015elj} shows that the time machine fails to work.
Essentially, the equivalence principle means that one shockwave jumps back in the background
of the other shockwave just before the particle jumps back. So the particle can never catch up
with the second shockwave: see the right-hand side of fig.~\ref{f2}.

Another way to think about this is that geometrically the classical time delay or advance is a coordinate-dependent
effect, which may be removed by working in Rosen-like coordinates where the particle trajectory is continuous
across the shock. The price to be paid is that in these new coordinates, the regions behind the shockwaves
are no longer manifestly flat. In order to assign a physical significance to the classical shift in the context of
scattering, we therefore need to impose some external identification of the asymptotically past and future
Minkowski space regions.

\subsection{Curvature couplings and the effective theory}

To motivate our discussion, consider first the case of graviton scattering. Here, the effective action
considered by \cite{Camanho:2014apa} containing the Gauss-Bonnet term is
\EQ{
S_\text{eff}=\frac1{16\pi G}\int d^dx\,\sqrt{g}\big[R+\alpha\big(R^2_{\mu\nu\rho\sigma}-
4R_{\mu\nu}^2+R^2\big)+\cdots\big]\ ,
}
which is non-trivial when $d\neq4$.
The Gauss-Bonnet coupling in the gravitational effective action violates the strong equivalence principle (SEP)
and the scattered graviton 1 no longer propagates along null geodesics. It induces a Shapiro time delay or advance
of the form  \cite{Camanho:2014apa}
\EQ{
\Delta v\sim\pm \alpha\frac{GE'}{b^{d-2}}\ ,
}
where the sign depends on the graviton polarization. In this case, the time delay or advance is a
genuine non-coordinate dependent effect that can be used to set up a causality paradox by using
the two-shockwave time machine described above.

This is analogous to the effective action generated in a self-interacting scalar QFT through the
coupling of a background graviton to the self-energy loop of the propagating scalar particle.
This induces a SEP-violating coupling to the Ricci tensor:\footnote{This is the scalar field equivalent of
the original Drummond-Hathrell effective action for QED in a background gravitational field, where
the effect of gravitational tidal forces inducing superluminal phase velocities at low frequency
was first discovered \cite{Drummond:1979pp}.}
\begin{equation}
S_\text{eff}= \int d^d x\,\sqrt{g} \left[-\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -
\frac{m^2}2\phi^2-\frac{\lambda}{n!}\phi^n-\alpha R^{\mu\nu}\partial_\mu \phi \partial_\nu \phi +\cdots\right]\ .
\label{cf1}
\end{equation}
Since in general the couplings $\lambda$ are dimensionful, it is convenient to define the
dimensionless coupling $\tilde{\lambda}$ as
\EQ{
\tilde\lambda=m^{2-p}\lambda ,  \qquad\qquad   p=\frac{(n-2)(d-2)}2\ .
\label{dimp}
}
The leading order contribution in perturbation theory is shown in fig.~\ref{f3} and leads to a coupling
\EQ{
\alpha=c_1\frac{\tilde\lambda^2}{m^2}\ ,
}
where $c_1$ is a {\it positive\/} number.
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=0.7,fill=black!20,decoration={markings,mark=at position 0.6 with {\arrow{>}}}]
\begin{scope}[xshift=0cm]
\draw[very thick] (-1.5,0) -- (0,0);
\draw[very thick] (2,0) -- (3.5,0);
\fill[very thick,pattern=north west lines,opacity=.6,draw] (1,0) circle [radius=1];
\draw[very thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (1,1) -- (1,2.5);
\end{scope}
\begin{scope}[xshift=9cm]
\node at (4.8,0) {$+\ \cdots$};
\node at (-3.6,0) {$=\qquad\cdots\ +$};
\draw[very thick] (-1.5,0) -- (0,0);
\draw[very thick] (2,0) -- (3.5,0);
\draw[very thick] (0,0) to[out=90,in=-180] (1,1) to[out=0,in=90] (2,0);
\draw[very thick] (0,0) to[out=-90,in=180] (1,-1) to[out=0,in=-90] (2,0);
\draw[very thick] (0,0) to[out=60,in=-180] (1,0.6) to[out=0,in=120] (2,0);
\draw[very thick] (0,0) to[out=-60,in=180] (1,-0.6) to[out=0,in=-120] (2,0);
\filldraw[black] (0,0) circle (2pt);
\filldraw[black] (2,0) circle (2pt);
\filldraw[black] (1,0.3) circle (0.8pt);
\filldraw[black] (1,-0.3) circle (0.8pt);\filldraw[black] (1,0) circle (0.8pt);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (1,1) -- (1,2.5);
\end{scope}
\end{tikzpicture}
\caption{\footnotesize The curvature-dependent coupling in the effective theory arises from one-graviton
corrections to the self energy, which at leading order in perturbation theory involve the diagram shown
where the graviton couples to one of the particles in the loops.}
\label{f3}
\end{center}
\end{figure}

Unlike the gravitational case, there is no polarization dependence here.
Nevertheless, for a background that satisfies the null energy condition, the coupling leads to a Shapiro time advance.
Note also that the shockwave produced by a high energy particle is a vacuum solution of Einstein's equation
and so is Ricci flat. However, one can consider the  related ``beam shockwave" \cite{Ferrari:1988cc},
described in detail in section \ref{s3}, that does have a non-vanishing Ricci curvature.
In this case one finds a time advance,
\EQ{
\Delta v=-c_2\tilde\lambda^2\frac{G\mu}{m^2}\ ,
\label{yy1}
}
where $\mu$ is the energy density of the beam and $c_2$ is a positive constant.
The particle shockwave produces a time advance at higher order in the curvature expansion.

The time shift is actually a completely generic effect for propagation in any non-Ricci flat background
as can be seen by solving the linearized equation of motion. Working
in the eikonal, or geometric optics, limit $E\gg m\gg\sigma$,
where $\sigma$ is the curvature scale of the shockwave expressed as an energy scale,
the solution for the field takes the form of a rapidly varying phase:
\EQ{
\phi(x)\thicksim\exp(-i\Theta(x))\ .
}
In this limit, the phase $\Theta(x)$ defines a congruence of null geodesics, corresponding to the rays
of geometric optics, whose tangent vector field
is $\partial^\mu\Theta$. It is always possible to introduce a set of adapted coordinates
$(u,V,X^i)$, $i=1,2,\ldots,d-2$, so that the congruence is described by
$V=\text{const.}$ and $X^i=\text{const.}$ and for which
\EQ{
\Theta(x)=EV\ .
}

Now consider the modifications implied by the curvature coupling in \eqref{cf1}.
Working in perturbation theory, we find that the phase receives an additional contribution
\EQ{
\Theta(x)=EV-\frac{\alpha E}2\int^u du\,R_{uu}(u)\ ,
}
where $R_{uu}(u)$ is a component of the Ricci tensor evaluated along the null geodesic $V=X^i=0$.
If the curved region is concentrated in an interval $[u_1,u_2]$, then the effect of the coupling is
to introduce a Shapiro time advance,
\EQ{
\Delta v=-\frac{\alpha}2\int_{u_1}^{u_2}du\,R_{uu}(u)\ .
}
The fact that this is an advance, {\it i.e.}~negative, is because the null energy condition
 implies that $R_{uu}\geq0$. It is also a fact, that we establish later, that $\alpha>0$.

Another way to think of this result is to notice that in the effective action \eqref{cf1}, it is as if the
field propagates in an effective metric ${\cal G}_{\mu\nu}=g_{\mu\nu}+\alpha R_{\mu\nu}$.
The particle's wave-vector $k_\mu=\partial_\mu\Theta$ is null with respect to this effective metric
but {\it spacelike\/} with respect to the real metric. This corresponds to superluminal propagation
and a Shapiro time advance.

\subsection{Beyond the effective action}

Our central theme is to address the question, in the context of scalar fields, of how these
curvature couplings impact on causality. A causality violating effect seen in the low energy theory is not,
in itself, a problem because such issues should be addressed in the UV limit.
The intuition here is that in order to send information from one place to another, it is necessary
to use sharp-fronted wave packets that inevitably require high frequency (energy) modes: these issue
are discussed at length in \cite{Shore:2007um}.
The question then is exactly how high does the energy have to be.
The point is that if the Shapiro time advance \eqref{yy1} is to be observable effect, we need that
\EQ{
E \Delta v>1\ .
}
If $\sigma$ is the curvature scale, which is proportional to $GE'/b^{d-2}$ for the particle shockwave,
then this requires $\tilde\lambda^2 E \sigma/m^2>1$.
This means that in order to access the UV limit necessary to discuss causality, we need
to be able to work in the regime where  $\tilde{\lambda}^2 \hat{s} > 1$,
where $\hat{s} = Gs/m^2 b^{d-2}$ is the dimensionless variable in the scattering phase introduced earlier.

Our main result will be to extend the determination of the scattering phase $\Theta_{\rm scat}(\hat{s})$
and Shapiro time advance
from the low-energy effective action to the UV limit where we can resolve issues with causality.
This calculation may be thought of as summing over the leading order self-energy diagram with an
arbitrary number of external gravitons attached as shown in fig.~\ref{f4}, which is equivalent to
calculating the original diagram with propagators defined in the curved shockwave geometry.
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=0.8,fill=black!20,decoration={markings,mark=at position 0.6 with {\arrow{>}}}]
\node at (-2.5,-0.8) {\footnotesize gravitons};
\node at (-2.5,0) {$\Large\displaystyle\sum$};
\draw[very thick] (-1.5,0) -- (0,0);
\draw[very thick] (2,0) -- (3.5,0);
\draw[very thick] (0,0) to[out=90,in=-180] (1,1) to[out=0,in=90] (2,0);
\draw[very thick] (0,0) to[out=-90,in=180] (1,-1) to[out=0,in=-90] (2,0);
\draw[very thick] (0,0) to[out=60,in=-180] (1,0.6) to[out=0,in=120] (2,0);
\draw[very thick] (0,0) to[out=-60,in=180] (1,-0.6) to[out=0,in=-120] (2,0);
\filldraw[black] (0,0) circle (2pt);
\filldraw[black] (2,0) circle (2pt);
\filldraw[black] (1,0.3) circle (0.8pt);
\filldraw[black] (1,-0.3) circle (0.8pt);
\filldraw[black] (1,0) circle (0.8pt);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (1,1) -- (1,2);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (0.5,0.5) -- (0,1.7);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (1.5,-0.5) -- (2,-1.7);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (0.5,-0.5) -- (0,-1.7);
\draw[thick,decoration={aspect=0.6, segment length=1.5mm, amplitude=0.8mm,coil},decorate] (2.5,0) -- (2.8,1.3);
\begin{scope}[scale=0.6,xshift=19cm,yshift=-3cm]
\node at (-10,3) {$=$};
\draw[line width=2mm,color=black!20] (-1,0) -- (-7,6);
\draw[very thick] (-7,0) -- (-5.5,1.5);
\draw[very thick]  (-2.5,4) -- (-1.5,6.4);
\draw[very thick,] (-5.5,1.5) to[out=30,in=-170] (-3.7,3.3);
\draw[very thick,] (-5.5,1.5) to[out=-40,in=-150] (-3.7,1.2);
\draw[very thick,] (-5.5,1.5) to[out=60,in=170] (-3.7,3.7);
\draw[very thick,] (-5.5,1.5) to[out=-80,in=-160] (-3.7,0.8);
\draw[very thick] (-3.7,3.3) to[out=10,in=160] (-2.5,4);
\draw[very thick] (-3.7,1.2) to[out=30,in=-120] (-2.5,4);
\draw[very thick] (-3.7,3.7) to[out=10,in=100] (-2.5,4);
\draw[very thick] (-3.7,0.8) to[out=30,in=-80] (-2.5,4);
\filldraw[black] (-5.5,1.5) circle (4pt);
\filldraw[black] (-2.5,4) circle (4pt);
\filldraw[black] (-4.3,2.6) circle (1pt);
\filldraw[black] (-4,2.1) circle (1pt);
\filldraw[black] (-3.7,1.6) circle (1pt);
\end{scope}
\end{tikzpicture}
\caption{\footnotesize The eikonal approximation can be extended by summing over diagrams
where an arbitrary number of gravitons are attached to the order $\lambda^2$ contribution to the self energy.
This is equivalent to evaluating the original diagram with propagators defined in the curved spacetime
as illustrated schematically in the right-hand figure.}
\label{f4}
\end{center}
\end{figure}

We are able to evaluate the self-energy diagram with curved space propagators given by the shockwave
geometry and determine the complete $\hat{s}$-dependence of the scattering phase.
Our results are valid for $E \gg m \gg \sigma$, where $\sigma\sim GE'/b^{d-2}$ for the particle shockwave
and $\sigma\sim G\mu$ for the beam shockwave.
We give an expression for the complete $\hat{s}$-dependence of $\Theta_{\rm scat}(\hat{s})$, focusing on the
low-energy regime $\hat{s} \ll 1$ which reproduces the effective action result, and on the high-energy,
regime where $\hat{s} \gg 1$. Notice that since $\hat{s}$ involves both the energy and impact parameter,
our calculation also allows us to access the small-$b$ scattering regime.

Self-interacting $\phi^n$ scalar field theories in arbitrary dimensions therefore provide a nice testing ground
for studying the effect of renormalizability on the realisation of causality in gravitational shockwave backgrounds,
complementing the discussion of QED in four dimensions in our recent paper \cite{Hollowood:2015elj}.
We will show that when a UV completion exists, that is when the spacetime dimension is at, or below,
the critical dimension $d\leq d_\text{crit}= 2n/(n-2)$ (equivalent to $p=2$ in (\ref{dimp})),
{\it i.e.}~in the renormalizable case,
the high energy limit of the Shapiro time advance goes to zero; causality is respected and a time machine
cannot be created. On the other hand, if $d>d_\text{crit}$, {\it i.e.}~the theory is non-renormalizable,
the Shapiro time advance persists and indeed diverges at the lowest order in perturbation theory.
(Of course, this does not necessarily rule out the possibility that causality could be repaired
at higher orders.) Within these broad categories, we will find differences in the $\hat{s}$-dependence
of the theories with various $n$ and $d$, reflecting power counting. These asymptotic behaviours
for the phase $\Theta_{\rm scat}(\hat{s})$ naturally also determine the scattering amplitude ${\cal A}(s,t)$
itself.

\section{The Eikonal Phase}\label{s2}

In this section, we calculate the contribution to the eikonal phase from the curved background
to leading order in perturbation theory (the calculation is similar to the analysis of QED
in \cite{Hollowood:2007kt,Hollowood:2007ku,Hollowood:2008kq,Hollowood:2009qz,
Hollowood:2010bd,Hollowood:2011yh}).

The task involves solving the linearized quantum corrected equation of motion.
\EQ{
\frac1{\sqrt{g}}\partial_\mu\Big(\sqrt{g}\,\partial^\mu\phi(x)\Big)-m^2\phi(x)=
\int d^dx\,\sqrt{g'}\,\Pi_\text{ret}(x,x')\phi(x')\ ,
\label{aa1}
}
in an appropriate approximation scheme. Note that $\Pi_\text{ret}(x,x')$ is the retarded
(Schwinger-Keldysh) self-energy or vacuum polarization calculated in the curved space background.
In order to solve \eqref{aa1}, it is necessary to define appropriate boundary conditions. This will be
described in more detail later.

To start with, we work in perturbation theory, beginning with a solution that describes a highly
relativistic particle with energy $E\gg m$ propagating along a null geodesic $\gamma$, or more
precisely a null congruence containing $\gamma$.
Associated with the congruence are a set of adapted coordinates $(u,V,X^i)$, $i=1,2,\ldots,d-2$,
such that $\gamma$ corresponds to $V=X^i=0$ and $u$ is the affine coordinate.

As well as working in perturbation theory, we make the additional approximation that
the mass of the field is much larger than the curvature scale $m\gg\mathfrak R$
(expressed as a mass scale) transverse to $\gamma$. The implication is that it is possible to approximate
the background geometry with that in a tubular neighbourhood of $\gamma$.
This is precisely the Penrose limit \cite{Penrose} of the metric associated to $\gamma$, which in terms
of the adapted coordinates takes the form
\begin{equation}
ds^2\Big|_{\text{Penrose}} =-2 du \,dV + C_{ij}(u) dX^i\, dX^j\ .
\label{bg}
\end{equation}

Once the null geodesic $\gamma$ has been picked out, the problem is to solve \eqref{aa1} in the
Penrose limit geometry in perturbation theory. The geometry \eqref{bg} is a plane wave and such
spacetimes are WKB, or eikonal, exact. This means that the solution of the wave equation and the
free Green functions are known exactly. Firstly, the solution of the wave equation takes the form
\EQ{
\phi(x) =g(u)^{-1/4}\exp\Big[-ip_-V -\frac i2p_+u+ ip_i X^i + \frac i{2E}p_i\psi^{ij}(u)p_j\Big] \ ,
\label{cb}
}
where
\EQ{
\psi^{ij}(u) = \int^udu\,[C^{-1}(u)]^{ij}\ .
\label{cc}
}
We will choose the solution with no transverse momentum $p_i=0$ and for an ultra-relativistic particle
$p_-=E\gg m$ and $p_+=m^2/E$:
\EQ{
\phi(x)=g(u)^{-1/4}\exp\Big[-iEV -\frac{im^2}{2E}u\Big]\ .
}
The idea, working in the eikonal approximation, is to search for a  solution of the quantum corrected
equation of motion \eqref{aa1} in the form
\EQ{
\phi(x)=g(u)^{-1/4}\exp\Big[-iEV -\frac{im^2}{2E}u+ i\Theta(u)\Big]\ .
}
Using the fact that the right-hand side is perturbatively small gives us the following equation for the
eikonal phase,
\EQ{
\partial_u\Theta(u)=\frac2E\int du'\,dV'\,d^{d-2}X'\,\big[g(u)g(u')\big]^{1/4}\,
\Pi(u,0;x')\exp\Big[\frac{im^2}{2E}(u-u')-iEV'\Big]
\label{ab2}
}

Now we consider the perturbative expansion of the vacuum polarization. There are various contributions
at order $\lambda$. These are independent of curvature and correspond to mass renormalization or are
cancelled by counter terms. The first important curvature-dependent contribution appears at order
$\lambda^2$: see fig.~\ref{f3} and fig.~\ref{f4}. We will limit ourselves to calculating the curvature
dependence of this diagram.

The contribution to the vacuum polarization from this diagram, in real space, is
simply\footnote{There are other contributions that serve to renormalize the operators $\phi^k$, $k<n$,
that do not affect the eikonal phase.}
\EQ{
\Pi(x,x')=\lambda^2 G(x,x')^{n-1}+\cdots\ ,
}
where $G(x,x')$ is the free propagator in the plane-wave background. One important point is that,
since we are integrating this against a positive energy mode, as in \eqref{ab2}, this automatically picks out
the retarded component of the vacuum polarization since the integral is only non-vanishing when $u'\leq u$.

In a plane-wave geometry, the Green function is known exactly,
\EQ{
G(x,x')=\sqrt{\Delta(x,x')}\int_0^\infty\frac{dT}{(4\pi iT)^{d/2}}\,i\exp\Big[-im^2T+\frac{\sigma(x,x')}{2iT}\Big]\ ,
\label{db}
}
where, in the Rosen coordinates $(u,V,X^i)$, the geodesic interval is
\EQ{
\sigma(x,x')=-(u-u')(V-V')+\frac12(X-X')^i\Delta_{ij}(u,u')(X-X')^j\ ,
\label{ab1}
}
where
\EQ{
\Delta_{ij}(u,u')=(u-u')\Big[\int^u_{u'}du''\,C^{-1}(u'')\Big]^{-1}_{ij}\ .
}
The other quantity in \eqref{db} is the Van Vleck-Morette VVM determinant which only depends on $u$ and $u'$
in a plane wave geometry:
\EQ{
\Delta(u,u')=\frac1{\sqrt{g(u)g(u')}}\det\Delta_{ij}(u,u')\ .
\label{vvm}
}

Looking at the form of \eqref{ab1}, it becomes clear the $X^{\prime i}$ integrals in \eqref{ab2} are Gaussian,
while the $V'$ yields a delta function. Before we perform these integrals, it is useful to change variables
from the proper times $\{T_i\}$, to the set $\{T,\xi_i\}$, where
\EQ{
T_i=T\xi_i\ ,\qquad\sum_{i=1}^{n-1}\xi_i=1\ .
}
where the parameters $\xi_i\in[0,1]$. We also define
\EQ{
\frac1{\zeta}=\sum_i\frac1\xi_i\ .
}
The relevant Jacobian is
\EQ{
\int\prod_{i=1}^{n-1}\frac{dT_i}{T_i^{d/2}}=\int\frac{dT}{T^{(n-1)(d/2-1)+1}}\prod_{i=1}^{n-1}
\frac{d\xi_i}{\xi_i^{d/2}}\,\delta\big(1-\sum_{i=1}^{n-1}\xi_i\big)\ .
}

The $V'$ integral yields a delta function:
\EQ{
\int dV'\,\exp\Big[\frac{(u'-u)V'}{2iT\zeta}-iE V'\Big]=4\pi T\zeta\delta\big(u'-u+2\zeta ET\big)\ ,
\label{ab3}
}
while the transverse coordinates yield
\EQ{
\int d^{d-2}X'\,\exp\Big[\frac i{4T\zeta}\,X^{\prime i}\Delta_{ij}(u,u')X^{\prime j}\Big]&=
\big(4\pi i\zeta T\big)^{(d-2)/2}\big(\det\Delta_{ij}(u,u')\big)^{-1/2}\\
&=\big(4\pi i\zeta T\big)^{(d-2)/2}(gg')^{-1/4}\Delta(u,u')^{-1/2}\ .
}

The delta function in \eqref{ab3}, can be used to exchange the $T$ integral for one over the separation
$t=u-u'$. Finally, after integrating over $u$,  we have the following expression for the eikonal phase
\EQ{
\Theta(u)=\frac{2^{p-1}i^{1-p}}{(4\pi)^{(n-2)d/2}}\lambda^2E^{p-2}\int d^{n-1}\xi\,\chi(\xi_i)
\int_{-\infty}^udu\,\int_0^{\infty-i0^+}\frac{dt}{t^p}\,e^{-izt}\Delta(u,u-t)^{(n-2)/2}\ ,
\label{bb1}
}
where
\EQ{
z=\frac{m^2}{2E}\big(\zeta^{-1}-1\big)
}
and
\EQ{
\int d^{n-1}\xi\equiv\int \prod_{i=1}^{n-1}d\xi_i\,\delta\big(1-\sum_i\xi_i\big)\ ,\qquad
\chi(\xi_i)=\zeta^{(n-1)(d-2)/2}\prod_{i=1}^{n-1}\xi_i^{-d/2}\ .
}

The prescription explicit in the definition of the $t$ integral is needed because the VVM determinant
can have singularities on the real $t$ axis and these must be avoided by moving into the lower half plane.

Before we turn to evaluating the phase, we first note that on physical grounds we must have $d\geq4$ and
so $p\geq1$. Note also that $p=2$ when $d=d_\text{crit}$. The expression in \eqref{bb1} has divergences
which can arise when $t\to0$, {\it i.e.}~$u\to u'$. These are the usual UV divergences that are expected
even in flat space.
When $d>d_\text{crit}$, we will see that there are new curvature-dependent UV divergences, as one might
have expected in a non-renormalizable theory.

There are also divergences that can arise when $u\to-\infty$. These arise from the way that \eqref{aa1}
is treated as an initial-value problem. The proper way to formulate the problem is in terms of the
Schwinger-Keldysh formalism as an initial value problem. In  a plane wave geometry, it is convenient
to work in the light front formalism and choose an initial value surface as the light front at some finite
$u=u_0$. The limit $u_0\to-\infty$ may be taken later. One way to choose boundary conditions is
to suppose that the interaction, which in this example is $\lambda\phi^n$, turns on abruptly at $u=u_0$.
In that case, the field is free for $u<u_0$ and when the coupling is turned on it becomed dressed in
real affine time for $u>u_0$. The picture is that a cloud of virtual quanta builds up around the bare state.
This process can have divergences that in the flat space theory are absorbed into wave function
renormalization. In curved space, there can be additional curvature-dependent divergences that require
additional wave function renormalization.

In order to disentangle the flat space and curvature-dependent divergences in \eqref{bb1},
we can separate out the curvature-dependent effects we are interested in by subtracting
the flat space contribution from \eqref{bb1}. This gives\footnote{In this equation
${\cal C}=2^{p-1}(4\pi)^{-(n-2)d/2}$ is a constant.}
\EQ{
\Theta(u)=\lambda^2{\cal C}i^{1-p}E^{p-2}\int d^{n-1}\xi\,\chi(\xi_i)
\int_{-\infty}^udu\,\int_0^{\infty-i0^+}\frac{dt}{t^p}\,e^{-izt}\big(\Delta(u,u-t)^{(n-2)/2}-1\big)\ .
\label{bbb2}
}
From now on, we will work with this subtracted phase. Also, it should be pointed out that $\Theta(u)$
has both real and imaginary parts. As far as questions of causality are concerned, we are interested
in the asymptotic value of the real part which gives the Shapiro time delay, or advance, via
\EQ{
\Delta v=\operatorname{Re}\frac{\Theta}E\ ,\qquad \Theta_\text{scat}=\Theta(u\to\infty)\ .
}

\section{Shockwave Geometries}\label{s3}

The Aichelburg-Sexl metric for a gravitational shockwave, in $d$ dimensions,
is given in \eqref{ba}.\footnote{In terms of Cartesian coordinates, we take $u=\frac12(t+z)$ and
$v=t-z$.} The profile function $f(r)$ is determined by the Ricci curvature $R_{uu} = 8\pi G T_{uu}$
and depends on the nature of the matter source.

We will consider two kinds of source: (i) a particle
boosted into a frame where it has a large energy and, effectively, moves along a null geodesic
$v=x^j=0$ with an energy-momentum tensor $T_{uu} = E'\delta^{n-2}(x^i)\delta(u)$; and (ii) a beam
corresponding to a uniform energy density  boosted into the same frame so that $T_{uu}=\mu\delta(u)$.

The corresponding profiles $f(r)$ follow from the relation $R_{uu} = - \tfrac{1}{2} \Delta f(r)$,
where $\Delta$ is the $d-2$-dimensional Laplacian. This gives
\EQ{
\text{(particle)}:&\quad f(r)=\frac{4\Gamma(\frac{d-4}2)}{\pi^{\frac{d-4}2}}\cdot\frac{GE'}{r^{d-4}}\ ,\\
\text{(beam)}:&\quad f(r)=-\frac{8\pi G\mu}{d-2}r^2\ .
\label{bb}
}

The null geodesics corresponding to the trajectories of high energy particles propagating
in the $u$-direction in this background are well-known and display a discontinuous jump in the
Aichelburg-Sexl $v$ coordinate as the particle crosses the shockwave. In polar coordinates
for the transverse space,
\EQ{
v &= V + \frac{1}{2} f(R) \vartheta(u) + \frac{1}{8} f'(R)^2 u \vartheta(u)  \ ,\\
r &=  R+ \frac{1}{2} f'(R) u \vartheta(u) \ , \\
\phi^i&=\Phi^i   \ .
\label{bc}
}
$i=1,2,\ldots,d-3$ label the angular coordinates. The
$V,R,\Phi^i$ are constants labelling the individual geodesics in a null congruence: see fig.~\ref{f5}.
 \begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=1,decoration={markings,mark=at position 0.5 with {\arrow{>}}}]
\draw[very thick] (0.5,0.7) to[out=180,in=20] (-1,0);
\draw[very thick] (2.2,1.1) to[out=180,in=-10] (-1.2,1.5);
\draw[very thick] (2.7,3.2) to[out=180,in=-20] (-0.8,3.8);
\draw[very thick] (0.8,2.6) to[out=180,in=0] (-1.2,2.8);
\draw[very thick] (1.5,2) to[out=180,in=10] (-1,1.7);
\draw[fill=black!20,opacity=0.8] (0,0) -- (3,1) -- (3,4) -- (0,3) -- (0,0);
\draw[very thick,->] (0,0) -- (1,0.33333);
\draw[very thick,->] (0,0) -- (0,1);
\draw[very thick,->] (0.5,0.7) to[out=0,in=160] (3,0);
\draw[very thick,->] (2.2,1.1) to[out=0,in=-170] (5,1.5);
\draw[very thick,->] (2.7,3.2) to[out=0,in=-150] (5.5,3.8);
\draw[very thick,->] (0.8,2.6) to[out=0,in=150] (4.2,2.8);
\draw[very thick,->] (1.5,2) to[out=0,in=160] (4.8,1.7);
\filldraw[black] (0.5,0.7) circle (2pt);
\filldraw[black] (2.2,1.1) circle (2pt);
\filldraw[black] (2.7,3.2) circle (2pt);
\filldraw[black] (0.8,2.6) circle (2pt);
\filldraw[black] (1.5,2) circle (2pt);
\node at (0.7,-0.2) {$R,\Phi^i$};
\node at (-0.3,0.7) {$V$};
\node at (3.2,-0.1) {$u$};
\end{tikzpicture}
\caption{\footnotesize Adapted coordinates for a congruence of null geodesics.
The null coordinate $V$ and $d-2$ space-like coordinates $(R,\Phi^i)$ label the individual geodesics
in the congruence, while the other null coordinate $u$ plays the role of the affine coordinate along
the geodesics.}
\label{f5}
\end{center}
\end{figure}
They are therefore natural ``adapted coordinates'', in terms of which the Aichelburg-Sexl metric
can be rewritten as
\begin{equation}
ds^2 = - 2 du \,dV + \left[1 + \frac{1}{2}f''(R) u \vartheta(u)\right]^2 dR^2
+\left[1 + \frac{1}{2R} f'(R) u \vartheta(u)\right]^2 R^2 d\Phi^i\,d\Phi^i\ .
\label{bd}
\end{equation}

These geodesics describe straight, null trajectories in both half-planes $u<0$ and $u>0$
with a discontinuous coordinate shift $\Delta v= \tfrac{1}{2} f(R)$ and a deflection angle $\phi$,
with $\tan\phi/2 =  -\tfrac{1}{2}f'(R)$, at $u=0$. The full shockwave spacetime can therefore be viewed as
two Minkowski half-planes patched together along the surface $u=0$ with a displacement $\Delta v$.

Now, as discussed extensively in our earlier work, the effect of vacuum polarisation on the propagation
of a particle in a curved spacetime background depends on the geometry of geodesic deviation.
This is precisely the feature of the background that is encoded in the Penrose limit \cite{Penrose}
(see also \cite{Blau:2006ar}).
The Penrose limit is a plane-wave spacetime which is determined from the original spacetime metric
{\it and} a preferred geodesic. In a general spacetime, in adapted coordinates with preferred geodesic
$V = X^i = 0$, $i = 1,2,\ldots,d-2$, the metric may be written as
\begin{equation}
ds^2 = - 2 du\,dV + C(u,V,X^i) dV^2 + 2 C_i(u,V,X^i) dX^i\, dV + C_{ij}(u,V,X^i) dX^i\, dX^j \ .
\label{be}
\end{equation}
The Penrose limit is then
\EQ{
ds^2\Big|_\text{Penrose} = \lim_{\lambda\rightarrow0} ~~
\frac{1}{\lambda^2}~ ds^2(u,\lambda^2 V, \lambda X^i) = - 2 du \,dV + C_{ij}(u,0,0) dX^i \,dX^j  \ .
\label{bf}
}

For the Aichelburg-Sexl shockwave, we choose a preferred geodesic with impact parameter $b$,
{\it i.e.}~$V=0$, $R=b$, $\Phi^i=0$, so that $X^i = b\Phi^i$, $i=1,2,\ldots,d-3$,  $X^{d-2} = R-b$.
The Penrose limit is then \cite{Hollowood:2009qz}
\begin{equation}
ds^2\Big|_\text{Penrose} =~- 2 du \,dV + C_{ij}(u) dX^i\, dX^j \ ,
\label{bg}
\end{equation}
where
\EQ{
C_{ij}(u)=\big[1-\sigma_i u\vartheta(u)\big]^2\delta_{ij}\ ,
}
and we have defined
\EQ{
\text{(particle)}:&\quad\sigma_i\equiv\sigma=\frac{4\Gamma(\frac{d-2}2)}{\pi^{\frac{d-4}2}}
\cdot\frac{GE'}{b^{d-2}}\ ,\quad i=1,2,\ldots,d-3\ ,\\ &\quad \sigma_{d-2}=-(d-3)\sigma\ ,\\
\text{(beam)}:&\quad\sigma_i\equiv\sigma=\frac{8\pi G\mu}{d-2}\ ,\quad i=1,2,\ldots,d-2\ .
}
Note that in the particle case that $\sum_{i=1}^{d-2}\sigma_i=0$ which means that $R_{uu}=0$,
{\it i.e.}~the geometry is Ricci flat. This is to be expected, since the geometry is a vacuum solution
everywhere except at the position of the particle.

This is written in Rosen coordinates, which are well-suited to describing the geodesic congruence.
An alternative presentation is in terms of Brinkmann coordinates, where the metric is instantly
recognisable as a plane wave:
\EQ{
ds^2\Big|_\text{Penrose}=-2du\,dv  +\sum_{i=1}^{d-2}\Big[\sigma_ix^ix^i\delta(u)du^2 +dx^i\,dx^i \Big]\ .
\label{bi}
}
We will not have use for these coordinates in this paper.

The VVM determinant for this geometry is, from \eqref{vvm},
\EQ{
\Delta(u,u')=\prod_{i=1}^{d-2}\frac{|u-u'|}{|u-u'|+\sigma_iuu'}\ ,\quad uu'<0\ ,\qquad\Delta(u,u')=1\ ,
\quad uu'>0\ .
}
Note that $\Delta(u,u')$ is only non-trivial if $u$ and $u'$ lie on opposite sides of the plane of the shockwave.

\section{Analysing the Eikonal Phase}

In this section, we will investigate the eikonal phase for a shockwave spacetime.
The goal is to evaluate the eikonal phase $\Theta(u)$ in the asymptotic limit where $u\to\infty$,
since this is the quantity relevant for scattering.
In general, the $u$-dependence of $\Theta(u)$ exhibits interesting behaviour in its own right,
as explored in \cite{Hollowood:2015elj}, especially near the focal point of the null geodesic congruence.
Here, however, we are just interested in the scattering phase $\Theta_{\rm scat}(\hat{s}) =
\Theta(u\rightarrow\infty)$ and especially in its behaviour when the energy $E$ is small and large.

If we use the dimensionless coupling $\tilde\lambda$, the eikonal phase then depends only on the
dimensionless quantity $\hat{s}$ introduced above:
\EQ{
\Theta_\text{scat}=\tilde\lambda^2\,{\mathscr F}(\hat s)\ ,\qquad\hat s=\frac{\sigma E}{m^2}\ ,
}
so the regimes of low and high energy are more precisely defined in terms of $\hat{s}$,
\EQ{
\text{(Low energy):}\quad\hat s\ll1\ ,\qquad\text{(High energy):}\quad\hat s\gg1\ .
}

The expression for the subtracted phase is \eqref{bbb2} and so we simply have to take the
limit $u\to\infty$.
Note that for the shockwaves that $\Delta(u,u')=1$ when $u$ and $u'$ lie on opposite sides
of the shockwave. This means that in \eqref{bbb2} the $t$ integral can be taken to have a lower limit
$u$ and the lower limit of the $u$ limit can be taken to $0$:
\EQ{
\Theta_\text{scat}=\lambda^2{\cal C}i^{1-p}E^{p-2}\int d^{n-1}\xi\,\chi(\xi_i)
\int_0^\infty du\,\int_u^{\infty-i0^+}\frac{dt}{t^p}\,e^{-izt}\big(\Delta(u,u-t)^{(n-2)/2}-1\big)\ .
\label{bb3}
}

It is useful to reverse the order of the $t$ and $u$ integrals, using
\EQ{
\int_0^\infty du\int_u^{\infty-i0^+}dt=\int_0^{\infty-i0^+}dt\int_0^tdu\ .
}
Since the shockwaves just depend on one curvature scale $\sigma$, it makes sense to scale this
out of the integrals by taking $t\to t/\sigma$ and $u\to u/\sigma$. In addition, to take account
of the prescription on the $t$ integral, we rotate the contour $t\to-it$. Taking all this into account leaves
\EQ{
\Theta_\text{scat}=\tilde\lambda^2{\cal C}\hat s^{p-2}\int d^{n-1}\xi\,\chi(\xi_i)\,\int_0^{\infty}
\frac{dt}{t^p}\,e^{-\hat zt}J(t)\ ,
\label{bb2}
}
where $\hat z=z/\sigma=(\zeta^{-1}-1)/(2\hat s)$ is dimensionless.

In \eqref{bb2}, we have defined
\EQ{
\text{(particle):}&\quad J(t)=\int_0^tdu\,\Big[t^p\big(t+iu(u+it)\big)^{-p_1}
\big(t-i(d-3)\sigma u(u+it)\big)^{-p_2}-1\Big]\ ,\\[7pt]
\text{(beam):}&\quad J(t)=\int_0^tdu\,\Big[t^p\big(t+iu(u+it)\big)^{-p}-1\Big]\ ,
\label{bb3}
}
where $p_1=(n-2)(d-3)/2$, $p_2=(n-2)/2$ with $p_1+p_2=p$.

In the beam case, $J(t)$ can be evaluated for arbitrary $p$,
\EQ{
J(t)=&-\frac{2^{-p-1} it}{p-1}(y^{-1}-y)\Big\{(1+y)^{p-1}\, _2F_1\left(1-p,p,2-p;
\tfrac12(1-y)\right)\\ &-
(1-y)^{p-1}\, _2F_1\left(1-p,p,2-p;\tfrac12(1+y)\right)\Big\}+it\ ,
\label{uur}
}
where $y=(1+4i/t)^{-1/2}$. For the particle case, $J(t)$ can be evaluated for particular $p$ but the
expressions are cumbersome and we will not write them here.

In \cite{Hollowood:2015elj}, we presented a number of numerical plots of the corresponding results
for QED to illustrate the full $\hat{s}$-dependence of the phase and how it interpolates between the
low-energy and UV limits. Here, we are most interested in the limiting behaviours and their relevance
for causality, so we present only these results below.

\subsection{Low energy expansion}

The expansion in the energy $E$, or equivalently the curvature, follows from expanding $J(t)$
in powers of $t$:
\EQ{
\text{(particle):}&\quad J(t)=i\frac{(n-2)(d-2)(d-3)}{120}t^3-\frac{(n-2)(d-2)(d-3)(d-4)}{840}t^4+
\cdots\ ,\\[7pt] \text{(beam)}:&\quad J(t)=-\frac{p}{6}t^2+i\frac{(p+1)p}{60}t^3+
\frac{(p+2)(p+1)p}{840}t^4+\cdots\ .
}

We can then perform the $t$ integral on each of the terms above separately, using
\EQ{
\int_0^{\infty}dt\,e^{-\hat z t}t^a=\hat z^{-a}\Gamma(1+a)\ .
}
The expansion of the eikonal phase consequently takes the form
\EQ{
\Theta_\text{scat}=-b_1\Gamma(3-p)\tilde\lambda^2\hat s+ib_2\Gamma(4-p)\tilde\lambda^2\hat s^2-
b_3\Gamma(5-p)\tilde\lambda^2\hat s^3+\cdots\ .
\label{hh1}
}
The coefficients $b_i$ are positive real numbers depending on $d$ and $n$. The gamma functions
in this formula encode the UV structure of the theory. Divergences appear when $p>2$,
in other words when $d>d_\text{crit}$.
So when the theory becomes  non-renormalizable there are additional curvature dependent divergences.
These can be regularized with additional curvature-dependent counterterms.

We recognize the first term in \eqref{hh1} as $E\Delta v$, with the Shapiro time advance
in \eqref{yy1}. This term is absent for the particle shockwave because that geometry is a
vacuum solution and so is Ricci flat. We have therefore recovered the effective action prediction
as the low-energy limit of our general result.

\subsection{High energy expansion}

The large $E$ behaviour is encoded in the large $t$ behaviour of $J(t)$. This is ${\mathscr O}(t^{1-p})$,
therefore when $p>2$, that is $d>d_\text{crit}$, the $t$ integral is convergent at its upper limit when
$\hat z=0$. The lower limit $t\to 0$ is divergent. These are the UV divergences already identified.
In order to make these completely explicit, we will introduce
an explicit high-momentum Euclidean cut off $\Lambda$. This appears as a cut-off on the lower limit
of the $T$ integral of $-i\Lambda^{-2}$ which becomes a cut-off on the lower limit of the $t$ integral
of $2i\zeta E/\Lambda^2$. After the re-scaling and analytic continuation, this becomes
$\delta=2\zeta\sigma E/\Lambda^2$.

So when $d>d_\text{crit}$, that is $p>2$, we have
\EQ{
\int_\delta^\infty \frac{dt}{t^p}\,J(t)=\text{const.}+\sum_{j=1}^{[p-2]}c_j\delta^{p-2-j}\ ,
}
where the $j=p-2$ term, if present, is $\delta^0\to\log\delta$.
So assuming that the UV divergences are cancelled by counterterms, the high energy behaviour is simply
\EQ{
(p>2):\qquad\Theta_\text{scat}=\tilde\lambda^2\tilde{\cal C}\hat s^{p-2}+{\mathscr O}(\hat s^{p-3})\ .
\label{gtt1}
}
for a complex constant $\tilde{\cal C}$.

When $d\leq d_\text{crit}$, that is $p\leq2$, there are no UV divergences. However, the $t$ integral
is no longer convergent at its upper end when $z=0$. This means that the behaviour is richer than
$E^{p-2}$. We find
\EQ{
(p=2):\qquad&\Theta=\tilde\lambda^2\big(-\tilde{\cal C}_1+
i\tilde{\cal C}_2\log\hat s+{\mathscr O}(\hat s^{-1}\log\hat s)\big)\ ,\\[3pt]
(p=\tfrac32):\qquad&
\Theta=\tilde\lambda^2\big(-\tilde{\cal C}_1\hat s^{-1/2}+i\tilde{\cal C}_2+
{\mathscr O}(\hat s^{-3/2})\big)\ ,\\[3pt]
(p=1):\qquad&\Theta=\tilde\lambda^2\big(-\tilde{\cal C}_1\hat s^{-1}\log^2\hat s+
i\tilde{\cal C}_2+{\mathscr O}(\hat s^{-2}\log^2\hat s)\big)\ .
\label{gtt2}
}
where the $\tilde{\cal C}_i$ are real positive constants.

The high energy behaviour \eqref{gtt1} and \eqref{gtt2} of the eikonal phase is our main result.
Physically, we have $d\geq4$, so the results apply to a variety of $\phi^n$ theories in different
dimensions:
$\phi^3$ theories in $d=4$ ($p=1$), $d=5$ ($p=3/2$), $d=6$ ($p=2$) and $d>6$ ($p>2$);
$\phi^4$ in $d=4$ ($p=2$), and $d>4$ ($p>2$);
and $\phi^n$ for $n>4$ in $d>4$ ($p>2$).

It is then apparent that when the theory is (perturbatively) renormalizable, $p\leq2$,
the eikonal phase remains perturbatively bounded. So in this case the theory has a good UV completion
and in the high energy regime the Shapiro time advance goes to zero:
\EQ{
(p\leq2):\qquad\Delta v(E\to\infty)=0\ .
}
The Shapiro time advance induced by the Ricci term in the effective action \eqref{cf1} therefore does
{\it not} lead to causality paradoxes.

On the other hand, above the critical dimension, $p>2$ and the eikonal phase grows at high energy.
The causality problems are therefore not resolved and at some point perturbation theory breaks down.
This is an indication that the lack of a well-defined UV completion implies that the causal problems inherent
in the low energy effective action are not resolved at high energy.

\section{Summary and Outlook}

In this paper, we have studied ultra-high energy scattering in scalar QFTs with different renormalizability properties
in order to shed further light on the relation of causality to the existence of a UV completion and how the
apparent causal paradoxes arising in the associated effective theories are resolved.
As is well-known, the leading eikonal approximation for the scattering amplitude ${\cal A}(s,t)$ at Planck energies
may be found by studying the propagation of a null particle in an Aichelburg-Sexl shockwave background.
At tree level in the QFT, the particle experiences a discontinuous lightcone coordinate shift as it passes
through the shockwave wavefront, and the corresponding phase shift $\Theta_{\rm cl}(s,b)$ gives rise to
the familiar leading-order approximation (\ref{a2}) to ${\cal A}(s,t)$.

We may go beyond this by considering vacuum polarization loop corrections in the QFT. These introduce a
new scale $\lambda_c$ characterising the size of the virtual cloud on which the gravitational tidal forces act.
At low energies, below the Planck scale, these can be described by an effective action, which violates the
strong equivalence principle and in general exhibits superluminal causality violations and Shapiro time
advances.

In our recent paper \cite{Hollowood:2015elj}, we showed how this issue is resolved in shockwave backgrounds
by explicitly computing the loop corrections $\Theta_{\rm scat}(\hat{s})$ to the scattering phase for all energies.
As we have seen, this depends only on the single variable
$\hat{s} = Gs/m^2 b^2 = \left(s/M_p^2\right)\left(\lambda_c/b\right)^2$
(in four dimensions) combining the energy and impact parameter.

This calculation is made tractable by the fact that we can use the Penrose limit of the full shockwave
background in order to perform the loop calculations.  This is because the Penrose limit encodes the geometry
of geodesic deviation in a tubular neighbourhood of the null trajectory traced out at tree level by the scattered
particle. This technology allows us to extend the evaluation of the scattering phase and coordinate shifts
beyond the effective theory approximation and into the UV limit necessary to address questions of causality.

In this paper, which complements \cite{Hollowood:2015elj}, we have extended these calculations to compute
the scattering phase shifts $\Theta_{\rm scat}(\hat{s})$ in a variety of self-interacting scalar QFTs with different
renormalizability properties. This allows us to investigate in detail the relationship between causality and
the existence of a well-defined UV completion.

Our main conclusions are summarized in (\ref{gtt1}) and (\ref{gtt2}).
For the strictly renormalizable theories, we find the perhaps initially surprising result that the scattering phase
does not go to zero in the high-energy limit, but goes asymptotically to a negative constant.
This is, however, still compatible with causality since the corresponding coordinate shift
$\Delta v$ given by (\ref{zz1}) does indeed vanish in this limit. This precludes the possibility of
constructing a time machine using the shockwave geometry and causality is respected.
For super-renormalizable theories, the real part of the phase vanishes in the UV limit, with the high
$\hat{s}$ behaviour of $\Theta_{\rm scat}(\hat{s})$ depending on the power-counting parameter $p$
as shown in (\ref{gtt2}).
Finally, for non-renormalizable theories above the critical dimension, we find the phase
$\Theta_{\rm scat}(\hat{s})$ goes like a positive power of $\hat{s}$ in the UV limit. This implies a
non-vanishing Shapiro time advance even at high energy and is a true violation of causality.

This establishes quite explicitly the expected link between good causal behaviour of the
scattering amplitude and the existence of a well-defined UV completion of the QFT.
Note also that the imaginary parts of the phases quoted in (\ref{gtt2}) contribute directly
to the magnitude $\left|{\cal A}(s,t)\right|^2$ of the scattering amplitude.

These results for $\Theta_{\rm scat}(\hat{s})$ determine the scattering amplitude ${\cal A}(s,t)$
from (\ref{a1}) and (\ref{a3}). It would be interesting to investigate further exactly how the energy and
impact parameter dependence we have found here for the phase as a consequence of QFT loop effects
is reflected in the causality and unitarity properties of ${\cal A}(s,t)$ itself.

Finally, it would be interesting to compare these results in more detail with graviton scattering
in string theory, where the string scale $\lambda_s$ plays a r\^ole apparently analogous to that
of $\lambda_c$ in the QFT case. Here, the reggeization of the scattering amplitude characteristic
of string theory provides the necessary causal UV completion for graviton scattering, where the
analogous effective action also exhibits causality violation \cite{Camanho:2014apa,D'Appollonio:2015gpa}.

\section*{Acknowledgements}

\noindent This research was supported in part by STFC grant
ST/L000369/1.  We are grateful to Gabriele Veneziano for helpful
discussions and correspondence and the TH Division, CERN for hospitality
during key stages of this work.

redpajama_set_name: RedPajamaArXiv


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KEEP UP TO DATE: Coronavirus (COVID-19)
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Overall Purpose: The Artwork Planner will be responsible for planning and purchasing activities for the Athlone manufacturing site with particular focus on revision controlled printed packaging components. This will include the development of Artwork planning and purchasing systems, vendor management systems and sourcing of goods and services.
This is an important role for a start-up site as the systems of work need to be built from the bottom up while the Artwork Planner works with technical personnel to source supply of printed packaging components in addition to other materials and services required to support plant qualification and full commercialisation.
The Artwork Planner in conjunction with the Supply Chain Manager will develop the site's lean supply chain systems to support commercialisation of the companies new ophthalmic products. The successful candidate will also work with Supply Chain colleagues globally to ensure the Athlone site plays the key role in companies global supply chain.
The successful candidate will also be responsible to ensure specific artwork planning and purchasing systems strive to deliver best value for the organisation across goods and services procured.
The role reports to the site's Supply Chain Manager.
Key areas of responsibility that the Artwork Planner will be held accountable for include hands-on participation in supply chain department activities such as Demand Management and Customer service, Manufacturing Planning for the Athlone facility, Raw material purchasing and Business & Quality Compliance. Tasks to be completed will encompass all of the department activities listed above. Other site function and customer interactions and must follow supply chain best practices.
Process customer orders as per the current department procedures and issue customers with order confirmations detailing pricing and expected delivery dates.
Provide customers business updates on agreed formats and frequencies while ensuring accurate and prompt responsiveness to customer inquiries.
Direct requests and unresolved client issues to the appropriate designated resource.
Keep clear and concise records of customer interactions and transactions.
Collate forecasting data on a monthly basis from customers and present clear and consolidated demand picture to the wider business.
Participate by taking a lead role at planning meetings and liaise directly with all groups involved in the manufacturing process - e.g. Operations, QC, QA, & Tec Services as appropriate to resolve operational issues as they arise.
Establish manufacturing requirements and monitor adherence to schedule reporting variances in a timely and business appropriate manner.
Provide guidance to R&D during product development projects on manufacturing facility supply chain requirements for best cost/lead time in a commercial environment.
Plan and implement activities related to the timely cost-effective inventory control, planning and quality control of production and R&D materials.
Participate by taking a lead role with respect to the Purchasing and Management of Printed Packaging components.
Interface directly with all departments on site to ensure that materials that are required to support Manufacturing schedules are available as required.
Ensure that Purchase specifications are in place prior to purchasing materials and liaise directly with suppliers with respect to delivery schedules.
Execute Supplier negotiations for best total cost, lead-times and terms for the business.
Ensure that purchase orders are used to secure goods and services on behalf of the company.
Ensure that at all times any tasks being completed is done in a manner that is fully compliant with all Quality requirements and Business guidelines.
Present, where appropriate, any information (technical or otherwise) requested by internal audit groups, external audit groups or other functional departments on site.
Develop policies and procedures as requested in the areas of Artwork Management, procurement, supplier management, Inventory Management, storage and distribution of materials and finished goods.
Complete all assigned training on time.
Close out all assigned quality notifications on time and to the standard expected by quality.
Adhere to company policies, procedures, and ethics codes and ensure that they are communicated and implemented within the department.
Communicate and coordinate with internal & external departments.
Deliver continuous improvement in supplier delivery, quality and cost.
Ability and flexibility to perform all other job-related and ad-hoc duties as required.
Solid business acumen with strong analytical and problem-solving skills. Strong organizational skill set.
Demonstrated successes in a team environment, such as project teams and continuous improvement teams.
Ability to work positively with global supply chain colleagues in the interest of the site and organisation.
Appreciation of the different challenges of start-up and subsequent commercialisation of a new pharmaceutical manufacturing facility.
Degree or 3rd level qualification (Science, Engineering, Business, Supply Chain).
APICS or other related procurement qualification.
8+ professional Artwork specific Purchasing and planning experience in a multinational manufacturing organisation.
Experience of ERP solutions used within global manufacturing organisations including integration of Serialisation requirements.
Experience managing vendor relationships, monitoring vendor performance and improving this performance.
Ideally, experience working in a start-up environment and therefore in establishing systems without the ability to leverage existing business processes.
Working experience and understanding of GMP regulations and GDP requirements.
Experienced in dealing with multi-site relationships and interactions with a high level of Customer Service orientation/understanding.
Excellent working knowledge of Microsoft applications essential.


It's in progress. Algernon is an open source project where I am the main contributor, and I develop Algernon in my spare time. Pull requests are welcome.
I'd love to help, but my coding time is already taken building a product.
I didn't believe it could be that simple, but it worked first time and has proven really robust.
// encrypted HTTPS with HTTP->HTTPS redirects - yay!
"Files that are sent to the client are compressed with gzip, unless they are under 4096 bytes."
That's interesting. Is that a common optimization? I hadn't heard of any other web server doing that.
I did some quick benchmarking and for files under roughly 4096 bytes, not compressing with gzip was faster.
It's not terribly exact, +-1000 bytes would probably not make a big difference, but I think it's a good default.
And of course, some people may have unique use cases where a custom threshold may be better.
Nginx uses a similar optimization with a configurable threshold defaulted to 1kb.
I heared somewhere (Some blogs comment section, I believe) that gzip actually reduces the security of HTTPS; maybe someone can confirm / explain that?
Compression technologies, including gzip, obviously have the goal of making things smaller by predicting later data based on earlier data. If the later data looks more like the earlier data, the result is smaller than if it was random gibberish. Compression!
If an attacker controls /some/ of this data, and would like to read /other parts/, they can abuse compression to measure whether the parts they don't know are "like" the part they control, because if they are then the compression will make the results shorter than otherwise which they can passively measure.
It's not a problem to move a compressed object over a secure channel on its own, the problem arises if either you try to compress the channel which is moving objects from different origins (e.g. a cookie set by a random advertising web site and your Facebook password) or compress a composite object e.g. maybe your backups mixed with a file you downloaded from a dodgy "pirate" video site.
In scenario when an attacker can see encrypted message (e.g. monitoring network traffic) and can affect part of the message that is being encrypted, he can use the compression to his advantage. He can for example try different inputs and observe the length of encrypted message, if with the certain input the length drops that means the given input contains string that's similar to another part of the decrypted message and the compressing algorithm did its job and used that to reduce the size.
This shouldn't be true in any sane system.
I'd be surprised if it didn't exist in every compression middleware.
I don't see anything like that documented for apache's mod_deflate/zlib.
Seems not, but there is for mod_gzip for example. I'd definitely consider it common.
Also, according to the spec HTTP servers may not always honour the value in the `Accept-Encoding` header.
> Even if both the client and the server supports the same compression algorithms, the server may choose not to compress the body of a response, if the identity value is also acceptable.
Makes more sense to use the verb "negotiating" with Accept-* headers rather than "honoring".
This makes obvious sense once you consider that the client tells the server which compression formats it supports in every request yet not every data format is compressible, nor does the server necessary support any candidate compression format.
For example, the server wouldn't gzip a jpeg since it's already compressed.
All Accept-* headers are like this. e.g. the server doesn't necessarily support any of the languages requested in the Accept-Language header, but it doesn't hurt to ask. You always have to inspect the response headers to see the result of negotiation.
"Accept-Encoding" means only that the client also understands specific encoding (in this case compression) it is still up to the server to chose what to dot. There was a time when browsers didn't support any compression. This header was introduced to signal to server what is acceptable by the client, that's why the header allows specifying multiple compression algorithms.
Similar thing is with header that's quite useful, but for some reason very few sites honor it: "Accept-Language" browser can specify which languages are preferred, but it is up to server to honor it (for example given language version is not available).
> The file size must be between 1,000 and 10,000,000 bytes.
Tomcat, one of the most used Java application servers and the default server behind Spring Boot applications defaults to a "compressionMinSize " value of 2048.
The docs do not explain why.
So yet another reason to think about 'what to gzip'.
Applications that always know exactly what they want to send disable this algorithm, as that article explains, by setting TCP_NODELAY or its moral equvialents in their framework. A web server will almost invariably set TCP_NODELAY.
More sophisticated algorithms can either decide exactly which packets to send, or use TCP_CORK to shove part of a packet into a buffer before they add the rest of the stuff, e.g. preparing HTTP headers and then adding the static document that goes after them.
If you read the page you linked, it says the algorithm applies to data of any size.
I don't know about "under 4096 bytes" but I have heard of not compressing data that is under ~1500 bytes. Part of the thinking is this - if your result data (plus HTTP overhead) is already smaller than the data payload of an IP packet (MTU settings come into play here), then you are spending CPU time that will not save you any network I/O time.
Yes, also compressing and decompressing a small amount of bytes may take longer than just sending it uncompressed.
> All in one small self-contained executable.
For self-contained architecture-specific server binaries, there is no practical difference between 240KB, or 2.4MB, or 24.4MB, or even, at a stretch, 244MB. It's not worth mentioning or optimizing for, except as novelty. I wish people would stop golfing with these numbers.
You have it backwards, apache or nginx size is not for the novelty. Go is just a pig and its size grows every new release, and the size isn't really for being statically linked or debugging symbols, because it's huge even when those options are disabled.
Right now a "hello world" application in Go has comparable size to an OS with full GUI.
You would need find an application where the binary image size is a problem. In an age where 1TB SSDs are 300 USD this will be ... challenging. You are able to have about a thousand gigabyte sized images on that one SSD and I suspect you will hit CPU and I/O limits well before you have a thousand different binaries running for real.
Media storage would go on spinning rust disks anyways separate from the SSD(s).
The consideration isn't binary size, but hot-loop cache coherency. Big binaries cause code-segment cache-line eviction.
Then that's a typical case of optimizing on the wrong metric.
Find a case where it's actually too slow, ok, but saying "A does X, and X can lead to Y, therefore A does Y" is wrong.
If you say the size of the binary is an issue, then give the issue, not how it could (or not) be an issue.
We observed noticeable difference in deployment time and auto scaling based on container size.
Who cares? Literally, what problem does it cause, or what does it make worse? It is totally immaterial.
True. Luckily, most Go binaries can be upx'd ( https://upx.github.io/ ) for a fraction of their original size. Just put it into your Dockerfile as a part of the build process.
This works and helps with storage/transit. Word of warning though that many AV like to flag UPX'd executables (only important if it's not an internal tool), and it'll take even longer for it to start, and will use more memory. My understanding is it essentially does standard compression on the executable and appends the decompression part on the front of it.
With UPX the entire docker image with Algernon takes only 9MB.
You have to ask yourself what is that space used for??
They're all compiled languages doing (roughly) the same operations. There is an order of magnitude difference in the number of instructions in one compared to the other.
Apache is more likely to be entirely cached whereas the others aren't.
Size matters for performance.... if you're not CPU bound, fine, but to say its immaterial is naive.
Even if we don't know which particular problem it might cause right now, being wasteful when you can avoid it is never a good idea.
Image size is currently not the most important metric, but - guessing how your average node.js package already looks today - demanding people ignore it completely will probably set you on the road of multi TB images that also contain the developer's favorite desktop environment in the medium future.
Hopefully we can get smaller binaries by Go 1.13.
My Apache installation with modules takes 4.3MB, and I'm quite sure Apache with modules can do more than Algernon.
If that's the main criticism you have of the project, I'd say that's pretty good.
In fact, the readme of this project is really thorough!
Very civilized comment from mr. Caddy himself. Heartening, not least considering the kind of vendettas some projects - Caddy among them - have to put up with from competing developers.
A big part is almost certainly the difference between dynamic and static linking.
Can you run ldd on all of these and then report the combined size for each binary+libraries?
As someone else commented, the huge size of Go executables is down to a design decision to include a map of functions for panic reporting. There was a whole discussion on this recently on HN.
I don't know why the grandparent was downvoted. Go binaries are not small and the claim that this is a "small" single executable is untrue.
Hopefully the Go team will give us a flag to decide for ourselves whether to optimise for executable size or initialisation time. I know I'm fed up of uploading 50Mb files over dodgy wifi+vpn connections to update my server.
which is useful, except as far as I'm aware it doesn't cover this case.
That's one thing that might motivate me to set up CI/CD on a server.
So 3.2 MB of shared library dependencies. 1.8 MB just being the libc which is almost guaranteed to be used by a different program already.
I don't think it is fair that you are being downvoted.
Size does matter and not just in sense that it is using resources. The largest part of the 24 MB probably never gets executed but it adds unnecessary complexity that may hide bugs and security flaws.
Algernon would be a lot smaller if it was not statically compiled and compiled with gccgo instead.
Sadly, the Go package that provides support for QUIC does not compile with gccgo, yet.
apache2 is mostly modules that are loaded at runtime.
How does this compare to OpenResty?
I suppose this one offers an all-in-one package, while openresty is really just an nginx server with builtin Lua(JIT) support.
What is the benefit of using this? In what scenario would this excel? Thanks.
Good question. I'm not sure if it excels in any scenario. There are specialized web servers that excel at caching or at raw performance. There are dedicated backends for popular front-end toolkits like Vue or React. There are dedicated editors that excel at editing and previewing Markdown, or HTML.
I guess the main benefit is that Algernon covers a lot of ground, with a minimum of configuration, while being powerful enough to have a plugin system and support for programming in Lua. There is an auto-refresh feature that uses Server Sent Events, when editing Markdown or web pages. There is also support for the latest in Web technologies, like HTTP/2, QUIC and TLS 1.3. The caching system is decent. And the use of Go ensures that also smaller platforms like NetBSD and systems like Raspberry Pi are covered. There are no external dependencies, so Algernon can run on any system that Go can support.
The main benefit is that is is versatile, fresh, and covers many platforms and use cases.
For a more specific description of a potential benefit, a more specific use case would be needed.