SV-map between Type I and Heterotic Sigma Models (1711.05821)
Wei Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor
Nov. 15, 2017 hep-th
The scattering amplitudes of gauge bosons in heterotic and open superstring theories are related by the single-valued projection which yields heterotic amplitudes by selecting a subset of multiple zeta value coefficients in the $\alpha'$ (string tension parameter) expansion of open string amplitudes. In the present work, we argue that this relation holds also at the level of low-energy expansions (or individual Feynman diagrams) of the respective effective actions, by investigating the beta functions of two-dimensional sigma models describing world-sheets of open and heterotic strings. We analyze the sigma model Feynman diagrams generating identical effective action terms in both theories and show that the heterotic coefficients are given by the single-valued projection of the open ones. The single-valued projection appears as a result of summing over all radial orderings of heterotic vertices on the complex plane representing string world-sheet.
Monodromy Relations in Higher-Loop String Amplitudes (1702.04963)
S. Hohenegger, S. Stieberger
Oct. 6, 2017 hep-th, math.AG, math.NT
New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point one-loop amplitudes described by a world-sheet cylinder (planar and non-planar) and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching alpha'-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.
Periods and Superstring Amplitudes (1605.03630)
S. Stieberger
May 11, 2016 hep-th, math.AG, math.NT
Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables. In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world-sheet given by the topology of a disk or sphere, respectively. Formally, for scattering of N strings this leads to N-3-dimensional iterated real integrals along the compactified real axis or N-3-dimensional complex sphere integrals, respectively. As a consequence the physical observables are described by periods on M_{0,N} - the moduli space of Riemann spheres of N ordered marked points. The mathematical structure of these string amplitudes share many recent advances in arithmetic algebraic geometry and number theory like multiple zeta values, single-valued multiple zeta values, Drinfeld, Deligne associators, Hopf algebra and Lie algebra structures related to Grothendiecks Galois theory. We review these results, with emphasis on a beautiful link between generalized hypergeometric functions describing the real iterated integrals on M_{0,N}(R) and the decomposition of motivic multiple zeta values. Furthermore, a relation expressing complex integrals on M_{0,N}(C) as single-valued projection of iterated real integrals on M_{0,N}(R) is exhibited.
Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering (1409.7405)
G. Dvali, C. Gomez, R.S. Isermann, D. Lust, S. Stieberger
Feb. 7, 2015 hep-th, gr-qc
We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the Kawai-Lewellen-Tye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole N-portrait. In particular, the perturbative suppression factor of a N-graviton final state, derived from the amplitude, matches the non-perturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by non-perturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including non-black hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the high-energy limit of the open and closed superstring tree-level scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different large-s and large-N regimes.
Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator (1310.3259)
Oct. 17, 2013 hep-th, math.NT
We revisit the tree-level closed superstring amplitude and identify its alpha'-expansion as series with single-valued multiple zeta values as coefficients. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Moreover, the alpha'-expansion of the closed superstring amplitude can be cast into the same algebraic form as the open superstring amplitude: the closed superstring amplitude essentially is the single-valued version of the open superstring amplitude. This fact points into a deeper connection between gauge and gravity amplitudes than what is implied by Kawai-Lewellen-Tye relations. Furthermore, we argue, that the Deligne associator carries the relevant information on the closed superstring amplitude. In particular, we give an explicit representation of the Deligne associator in terms of Gamma functions modulo squares of commutators of the underlying Lie algebra. This form of the associator can be interpreted as the four-point closed superstring amplitude.
Motivic Multiple Zeta Values and Superstring Amplitudes (1205.1516)
O. Schlotterer, S. Stieberger
Oct. 8, 2012 hep-th, hep-ph, math.NT
The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows to disentangle its alpha'-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the alpha'-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the alpha'-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the alpha'-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form.
BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form (1108.0323)
Nov. 15, 2011 hep-th, math.NT
We study BPS saturated one-loop amplitudes in type II string theory compactified on K3 x T^2. The classes of amplitudes we consider are only sensitive to the very basic topological data of the internal K3 manifold. As a consequence, the integrands of the former are related to the elliptic genus of K3, which can be decomposed into representations of the internal N=4 superconformal algebra. Depending on the precise choice of external states these amplitudes capture either only the contribution of the short multiplets or the full series including intermediate multiplets. In the latter case we can define a generating functional for the whole class, which we show is given by the weight ten Igusa cusp form chi_{10} of Sp(4,Z). We speculate on possible algebraic implications of our result on the BPS states of the N=4 type II compactification.
Higher Point Spin Field Correlators in D=4 Superstring Theory (0911.5168)
D. Haertl, O. Schlotterer, S. Stieberger
Oct. 8, 2011 hep-th
Calculational tools are provided allowing to determine general tree-level scattering amplitudes for processes involving bosons and fermions in heterotic and superstring theories in four space-time dimensions. We compute higher-point superstring correlators involving massless four-dimensional fermionic and spin fields. In D=4 these correlators boil down to a product of two pure spin field correlators of left- and right-handed spin fields. This observation greatly simplifies the computation of such correlators. The latter are basic ingredients to compute multi-fermion superstring amplitudes in D=4. Their underlying fermionic structure and the fermionic couplings in the effective action are determined by these correlators.
On tree-level higher order gravitational couplings in superstring theory (0910.0180)
We consider the scattering amplitudes of five and six gravitons at tree-level in superstring theory. Their power series expansions in the Regge slope alpha' are analyzed through the order alpha'^8 showing some interesting constraints on higher order gravitational couplings in the effective superstring action like the absence of R^5 terms. Furthermore, some transcendentality constraints on the coefficients of the non-vanishing couplings are observed: the absence of zeta values of even weight through the order alpha'^8 like the absence of zeta(2) zeta(3) R^6 terms. Our analysis is valid for any superstring background in any space-time dimension, which allows for a conformal field theory description.
Open & Closed vs. Pure Open String Disk Amplitudes (0907.2211)
June 23, 2010 hep-th
We establish a relation between disk amplitudes involving N_o open and N_c closed strings and disk amplitudes with only N_o+2N_c open strings. This map, which represents a sort of generalized KLT relation on the disk, reveals important structures between open & closed and pure open string disk amplitudes: it relates couplings of brane and bulk string states to pure brane couplings. On the string world-sheet this becomes a non-trivial monodromy problem, which reduces the disk amplitude of N_o open and N_c closed strings to a sum of many color ordered partial subamplitudes of N_o+2N_c open strings. This sum can be further reduced to a sum over (N_o+2N_c-3)! subamplitudes of N=N_o+2N_c open strings only. Hence, the computation of disk amplitudes involving open and closed strings is reduced to computing these subamplitudes in the open string sector. In this sector we find a string theory generalization and proof of the Kleiss-Kuijf and Bern-Carrasco-Johanson relations: All order alpha' identities between open string subamplitudes are derived, which reproduce these field-theory relations in the limit alpha'->0. These identities allow to reduce the number of independent subamplitudes of an open string N-point amplitude to (N-3)!. This number is identical to the dimension of a minimal basis of generalized Gaussian hypergeometric functions describing the full N-point open string amplitude.
The Hunt for New Physics at the Large Hadron Collider (1001.2693)
P. Nath, B.D. Nelson, H. Davoudiasl, B. Dutta, D. Feldman, Z. Liu, T. Han, P. Langacker, R. Mohapatra, J. Valle, A. Pilaftsis, D. Zerwas, S. AbdusSalam, C. Adam-Bourdarios, J.A. Aguilar-Saavedra, B. Allanach, B. Altunkaynak, L.A. Anchordoqui, H. Baer, B. Bajc, O. Buchmueller, M. Carena, R. Cavanaugh, S. Chang, K. Choi, C. Csaki, S. Dawson, F. de Campos, A. De Roeck, M. Duhrssen, O.J.P. Eboli, J.R. Ellis, H. Flacher, H. Goldberg, W. Grimus, U. Haisch, S. Heinemeyer, M. Hirsch, M. Holmes, T. Ibrahim, G. Isidori, G. Kane, K. Kong, R. Lafaye, G. Landsberg, L. Lavoura, J.S. Lee, S.J. Lee, M. Lisanti, D. Lust, M.B. Magro, R. Mahbubani, M. Malinsky, F. Maltoni, S. Morisi, M.M. Muhlleitner, B. Mukhopadhyaya, M. Neubert, K.A. Olive, G. Perez, P. Fileviez Perez, T. Plehn, E. Ponton, W. Porod, F. Quevedo, M. Rauch, D. Restrepo, T.G. Rizzo, J.C. Romao, F.J. Ronga, J. Santiago, J. Schechter, G. Senjanovic, J. Shao, M. Spira, S. Stieberger, Z. Sullivan, T.M.P. Tait, X. Tata, T.R. Taylor, M. Toharia, J. Wacker, C.E.M. Wagner, L.-T. Wang, G. Weiglein, D. Zeppenfeld, K. Zurek
Jan. 14, 2010 hep-ph
The Large Hadron Collider presents an unprecedented opportunity to probe the realm of new physics in the TeV region and shed light on some of the core unresolved issues of particle physics. These include the nature of electroweak symmetry breaking, the origin of mass, the possible constituent of cold dark matter, new sources of CP violation needed to explain the baryon excess in the universe, the possible existence of extra gauge groups and extra matter, and importantly the path Nature chooses to resolve the hierarchy problem - is it supersymmetry or extra dimensions. Many models of new physics beyond the standard model contain a hidden sector which can be probed at the LHC. Additionally, the LHC will be a top factory and accurate measurements of the properties of the top and its rare decays will provide a window to new physics. Further, the LHC could shed light on the origin of neutralino masses if the new physics associated with their generation lies in the TeV region. Finally, the LHC is also a laboratory to test the hypothesis of TeV scale strings and D-brane models. An overview of these possibilities is presented in the spirit that it will serve as a companion to the Technical Design Reports (TDRs) by the particle detector groups ATLAS and CMS to facilitate the test of the new theoretical ideas at the LHC. Which of these ideas stands the test of the LHC data will govern the course of particle physics in the subsequent decades.
The LHC String Hunter's Companion (II): Five-Particle Amplitudes and Universal Properties (0908.0409)
D. Lust, O. Schlotterer, S. Stieberger, T.R. Taylor
Nov. 23, 2009 hep-th, hep-ph, hep-ex
We extend the study of scattering amplitudes presented in ``The LHC String Hunter's Companion'' to the case of five-point processes that may reveal the signals of low mass strings at the LHC and are potentially useful for detailed investigations of fundamental Regge excitations. In particular, we compute the full-fledged string disk amplitudes describing all 2->3 parton scattering subprocesses leading to the production of three hadronic jets. We cast our results in a form suitable for the implementation of stringy partonic cross sections in the LHC data analysis. We discuss the universal, model-independent features of multi-parton processes and point out the existence of even stronger universality relating N-gluon amplitudes to the amplitudes involving N-2 gluons and one quark-antiquark pair. We construct a particularly simple basis of two functions describing all universal five-point amplitudes. We also discuss model-dependent amplitudes involving four fermions and one gauge boson that may be relevant for studying jets associated to Drell-Yan pairs and other processes depending on the spectrum of Kaluza-Klein particles, thus on the geometry of compact dimensions.
Resolved Toroidal Orbifolds and their Orientifolds (hep-th/0609014)
D. Lust, S. Reffert, E. Scheidegger, S. Stieberger
Dec. 18, 2006 hep-th
We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.
Moduli Stabilization in Type IIB Orientifolds (II) (hep-th/0609013)
D. Lust, S. Reffert, E. Scheidegger, W. Schulgin, S. Stieberger
We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.
Moduli Stabilization in Type IIB Orientifolds (I) (hep-th/0506090)
D. Lust, S. Reffert, W. Schulgin, S. Stieberger
We discuss flux quantization and moduli stabilization in toroidal type IIB Z_N - or Z_N x Z_M -orientifolds, focusing mainly on their orbifold limits. After presenting a detailed discussion of their moduli spaces and effective actions, we study the supersymmetric vacuum structure of these models and derive criteria for the existence of stable minima. Furthermore, we briefly investigate the models away from their orbifold points and comment on the microscopic origin of their non-perturbative superpotentials.
Amplitude for N-Gluon Superstring Scattering (hep-th/0607184)
S. Stieberger, T.R. Taylor
Oct. 4, 2006 hep-th, hep-ph
We consider scattering processes involving N gluonic massless states of open superstrings with certain Regge slope alpha'. At the semi-classical level, the string world-sheet sweeps a disk and N gluons are created or annihilated at the boundary. We present exact expressions for the corresponding amplitudes, valid to all orders in alpha', for the so-called maximally helicity violating configurations, with N=4, 5 and N=6. We also obtain the leading O(alpha'^2) string corrections to the zero-slope N-gluon Yang-Mills amplitudes.
Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums (hep-th/0509042)
D. Oprisa, S. Stieberger
Sept. 6, 2005 hep-th, math-ph, math.MP, math.NT
The six gluon disk amplitude is calculated in superstring theory. This amplitude probes the gauge interactions with six external legs on Dp-branes, in particular including e.g. F^6-terms. The full string S-matrix can be expressed by six generalized multiple hypergeometric functions (triple hypergeometric functions), which in the effective action play an important role in arranging the higher order alpha' gauge interaction terms with six external legs (like F^6, D^4 F^4, D^2 F^5, D^6 F^4, D^2 F^6, ...). A systematic and efficient method is found to calculate tree-level string amplitudes by equating seemingly different expressions for one and the same string S-matrix: Comparable to Riemann identities appearing in string-loop calculations, we find an intriguing way of using world-sheet supersymmetry to generate a system of non-trivial equations for string tree-level amplitudes. These equations result in algebraic identities between different multiple hypergeometric functions. Their (six-dimensional) solution gives the ingredients of the string S-matrix. We derive material relevant for any open string six-point scattering process: relations between triple hypergeometric functions, their integral representations and their alpha'-(momentum)-expansions given by (generalized) Euler-Zagier sums or (related) Witten zeta-functions.
MSSM with Soft SUSY Breaking Terms from D7-Branes with Fluxes (hep-th/0410074)
D. Lust, S. Reffert, S. Stieberger
July 3, 2005 hep-th, hep-ph
We discuss the structure of the soft supersymmetry breaking terms in a MSSM like model, which can be derived from D7-branes with chiral matter fields from 2-form f-fluxes and supersymmetry breaking from 3-form G-fluxes.
F-theory Flux, Destabilization of Orientifolds and Soft Terms on D7--Branes (hep-th/0501139)
D. Lust, P. Mayr, S. Reffert, S. Stieberger
Jan. 18, 2005 hep-th
We use F-theory to derive a general expression for the flux potential of type II compactifications with D7/D3 branes, including open string moduli and 2-form fluxes on the branes. Our main example is F-theory on K3 $\times$ K3 and its orientifold limit T^2/Z_2 x K3. The full scalar potential cannot be derived from the bulk superpotential W=\int \Omega \wedge G_3 and generically destabilizes the orientifold. Generically all open and closed string moduli are fixed, except for a volume factor. An alternative formulation of the problem in terms of the effective supergravity is given and we construct an explicit map between the F-theory fluxes and gaugings. We use the superpotential to compute the effective action for flux compactifications on orbifolds, including the \mu-term and soft-breaking terms on the D7-brane world-volume.
Flux-induced Soft Supersymmetry Breaking in Chiral Type IIB Orientifolds with D3/D7-Branes (hep-th/0406092)
We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric type IIB orientifold vacua with D3- and D7-branes. After a general discussion of possible choices of fluxes allowing for stabilizing of a part of the moduli, we determine the resulting effective action including all soft supersymmetry breaking terms. We also extend the computation of our previous work concerning the matter field metrics arising from various open string sectors, in particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the F-theory lift of our constructions is investigated.
Scattering of Gauge, Matter, and Moduli Fields from Intersecting Branes (hep-th/0404134)
D. Lust, P. Mayr, R. Richter, S. Stieberger
May 14, 2004 hep-th
We calculate various tree-level (disk) scattering amplitudes involving gauge, matter and moduli fields in type IIB toroidal orbifold/orientifold backgrounds with D9,D5 respectively D7,D3-branes or via T-duality D6-branes in type IIA compactifications. In type IIB the D-branes may have non-vanishing fluxes on their world-volume. From these results we extract the moduli and flux dependence of the tree-level gauge couplings, the metrics for the moduli and matter fields. The non-vanishing fluxes correspond in the T-dual type IIA description to intersecting D6-branes. This allows us to determine the moduli dependence of the tree-level matter field metrics in the effective action of intersecting D6-brane models. In addition we derive the physical Yukawa couplings with their correct normalization.
Gauge Threshold Corrections in Intersecting Brane World Models (hep-th/0302221)
D. Lust, S. Stieberger
Feb. 28, 2003 hep-th
We calculate the one-loop corrections to gauge couplings in N=1 supersymmetric brane world models, which are realized in an type IIA orbifold/orientifold background with several stacks of D6 branes wrapped on 3-cycles with non-vanishing intersections. Contributions arise from both N=1 and N=2 open string subsectors. In contrast to what is known from ordinary orbifold theories, N=1 subsectors give rise to moduli-dependent one-loop corrections.
Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems (hep-th/0209064)
Type I - heterotic duality in D=10 predicts various relations and constraints on higher order F^n couplings at different string loop levels on both sides. We prove the vanishing of two-loop corrections to the heterotic F^4 terms, which is one of the basic predictions from this duality. Furthermore, we show that the heterotic F^5 and (CP even) F^6 couplings are not renormalized at one loop. These results strengthen the conjecture that in D=10 any Tr F^(2n) coupling appears only at the disc tree-level on type I side and at (n-1)-loop level on the heterotic side. Our non-renormalization theorems are valid in any heterotic string vacuum with sixteen supercharges.
Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (I): Heterotic F^6 Terms at Two Loops (hep-th/0207026)
Sept. 30, 2002 hep-th
We study the two-loop F^6 interactions in SO(32) heterotic superstring theory in D=10. By using the generalized Riemann identity we are able to determine the single-trace part of the effective action up to a few constants which are related to certain scattering amplitudes. This two-loop heterotic result is related by duality to Type I interactions at the tree level. However, it turns out to be completely different from any sort of non-Abelian generalization of Born-Infeld theory. We offer an explanation of this discrepancy.
Divergences in Kaluza-Klein Models and their String Regularization (hep-th/0108183)
D.M. Ghilencea, H.P. Nilles, S. Stieberger
Aug. 24, 2001 hep-th, hep-ph
Effective field theories with (large) extra dimensions are studied within a physical regularization scheme provided by string theory. Explicit string calculations then allow us to consistently analyze the ultraviolet sensitivity of Kaluza--Klein theories in the presence or absence of low energy supersymmetry.