scholarly journals On genus-one string amplitudes on AdS5 × S5

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luis F. Alday
Keyword(s):  
Stress Tensor ◽  
Simple Structure ◽  
Strong Coupling Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Yang Mills ◽  
Space Limit ◽  
Type Iib String Theory ◽  
String Amplitudes ◽  
Genus One

Abstract We study non-planar correlators in $$ \mathcal{N} $$ N = 4 super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order 1/N4 and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on AdS5× S5 in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.

scholarly journals Maximal U(1)Y-violating n-point correlators in $$ \mathcal{N} $$ = 4 super-Yang-Mills theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Stress Tensor ◽  
Modular Forms ◽  
Flat Space ◽  
Low Energy ◽  
Superstring Theory ◽  
Recursion Relations ◽  
Yang Mills ◽  
Covariant Derivatives ◽  
Higher Derivative ◽  
Energy Expansion

Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1)Y-violating” correlators that violate the bonus U(1)Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1)Y-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS5× S5 at the same orders as R4, d4R4 and d6R4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1)Y-violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS5× S5.

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

scholarly journals Modular invariance in superstring theory from $$ \mathcal{N} $$ = 4 super-Yang-Mills

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Partition Function ◽  
Eisenstein Series ◽  
Correlation Functions ◽  
Flat Space ◽  
Modular Invariance ◽  
Point Function ◽  
Superstring Theory ◽  
Yang Mills ◽  
S Matrix ◽  
Space Limit

Abstract We study the four-point function of the lowest-lying half-BPS operators in the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N2− 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ E 5 2 τ τ ¯ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R4 and D4R4 contact inter-actions, which, for the R4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order $$ {N}^{\frac{1}{2}-m} $$ N 1 2 − m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant.

scholarly journals Two dialects for KZB equations: generating one-loop open-string integrals

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Johannes Broedel ◽  
André Kaderli ◽  
Oliver Schlotterer
Keyword(s):  
Differential Equations ◽  
Elliptic System ◽  
Configuration Space ◽  
Marked Point ◽  
Open String ◽  
Low Energy ◽  
Compatibility Conditions ◽  
Punctured Torus ◽  
String Amplitudes ◽  
Genus One

Abstract Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1–3]. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik-Zamolodchikov-Bernard(KZB) type on the twice-punctured torus.We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.

scholarly journals Color/kinematics duality in AdS4

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Connor Armstrong ◽  
Arthur E. Lipstein ◽  
Jiajie Mei
Keyword(s):  
Gauge Symmetry ◽  
Momentum Space ◽  
Flat Space ◽  
Yang Mills ◽  
Space Limit ◽  
Double Copy

Abstract In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS4. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS4 and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS4.

scholarly journals The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
H. Paul ◽  
M. Santagata
Keyword(s):  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Crossing Symmetry ◽  
String Correction ◽  
Space Limit ◽  
Fixed Order ◽  
Bootstrap Algorithm

Abstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators $$ {\mathcal{O}}_p $$ O p in $$ \mathcal{N} $$ N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS5× S5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS5× S5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS5 ↔ S5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

scholarly journals Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Tobias Hansen
Keyword(s):  
Gauge Group ◽  
Flat Space ◽  
Closed Form Expression ◽  
Tree Level ◽  
Modular Invariant ◽  
Higher Derivative ◽  
S Matrix ◽  
Space Limit ◽  
Type Iib String Theory ◽  
General Gauge

Abstract We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

scholarly journals Resolving spacetime singularities in flux compactifications & KKLT

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Federico Carta ◽  
Jakob Moritz
Keyword(s):  
Field Theory ◽  
Flux Compactifications ◽  
Effective Field Theory ◽  
Bound States ◽  
Effective Field ◽  
Low Energy ◽  
De Sitter ◽  
Yang Mills ◽  
Type Iib String Theory ◽  
De Sitter Vacuum

Abstract In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure SU(N) super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of n such exotic branes is given by the (A1, An−1) Argyres-Douglas theory. Moreover, the splitting of the perturbative (in α′) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $$ \mathcal{O} $$ O (1) Einstein frame volume. While this region generically takes up an $$ \mathcal{O} $$ O (1) fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential dynamically ensures that the 4d effective field theory of KKLT remains valid nevertheless.

UNIFICATION OF GRAVITY, GAUGE AND HIGGS FIELDS BY CONFINED QUANTUM FIELDS II-EFFECTIVE THEORY

1993 ◽  
Vol 08 (10) ◽  
pp. 947-960 ◽  
Author(s):  
TOSHIKI ISSE
Keyword(s):  
Flat Space ◽  
Low Energy ◽  
Effective Theory ◽  
Gauge Fields ◽  
Quantum Fields ◽  
Yang Mills ◽  
Free Fields ◽  
Higgs Fields

Dynamics of quantized free fields (of spin 0 and 1/2) contained in a subspace V* of an (N+4)-dimensional flat space V is studied. The space V* is considered as a neighborhood of a four-dimensional submanifold M arbitrarily embedded into V. We show that Einstein SO (N)-Yang-Mills Higgs theory is induced as a low energy effective theory of the system. Gravity, SO (N) gauge fields and Higgs fields are obtained from embedding functions of M.

scholarly journals Towards the Virasoro-Shapiro amplitude in AdS5×S5

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Theresa Abl ◽  
Paul Heslop ◽  
Arthur E. Lipstein
Keyword(s):  
Effective Field Theory ◽  
Flat Space ◽  
Effective Field ◽  
Tree Level ◽  
Yang Mills ◽  
Additional Information ◽  
Tree Level Amplitude ◽  
Covariant Derivatives ◽  
Type Iib String Theory ◽  
Single Trace

Abstract We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in $$ \mathcal{N} $$ N = 4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS5 × S5. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS5 × S5 whose coefficients are fixed by the flat space Virasoro-Shapiro amplitude up to ambiguities related to commutators of the 10d covariant derivatives which require additional information such as localisation. We illustrate this procedure by computing stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to $$ \mathcal{O} $$ O (α′7), and spell out a general algorithm for extending this to any order in α′.

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