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 On duality of color and kinematics in (A)dS momentum space

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Soner Albayrak ◽  
Savan Kharel ◽  
David Meltzer
Keyword(s):  
Wave Function ◽  
Analytic Continuation ◽  
Momentum Space ◽  
Spectral Representation ◽  
Flat Space ◽  
Tree Level ◽  
De Sitter ◽  
Yang Mills ◽  
The Universe ◽  
Double Copy

Abstract We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

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 Double copy structure and the flat space limit of conformal correlators in even dimensions

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Arthur E. Lipstein ◽  
Paul McFadden
Keyword(s):  
Flat Space ◽  
Space Limit ◽  
Double Copy

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 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 YANG–MILLS GRAVITY IN FLAT SPACE–TIME I: CLASSICAL GRAVITY WITH TRANSLATION GAUGE SYMMETRY

2006 ◽  
Vol 21 (25) ◽  
pp. 5119-5139 ◽  
Author(s):  
JONG-PING HSU
Keyword(s):  
Gauge Symmetry ◽  
Physical Space ◽  
Flat Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Metric Tensor ◽  
Yang Mills ◽  
Riemann Metric ◽  
Classical Particles ◽  
Tests Of Gravity

We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space–time with a new Yang–Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space–time. In the post-Newtonian approximation of the tensor gauge field produced by the energy–momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

scholarly journals Notes on flat-space limit of AdS/CFT

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Yue-Zhou Li
Keyword(s):  
Partial Wave ◽  
Momentum Space ◽  
Flat Space ◽  
Coordinate Space ◽  
Partial Wave Expansion ◽  
Wave Expansion ◽  
Space Limit ◽  
Space Coordinate

Abstract Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $$ \left\langle VV\mathcal{O}\right\rangle $$ VV O maps to photon-photon-massive amplitudes.

A non-abelian model SU(N) × SU(N)

2015 ◽  
Vol 8 (1) ◽  
pp. 1988-2004
Author(s):  
Renato Doria ◽  
M. J. Neves
Keyword(s):  
Gauge Symmetry ◽  
Momentum Space ◽  
Brst Symmetry ◽  
Power Counting ◽  
Physical Application ◽  
Tree Level ◽  
Color Symmetry ◽  
Yang Mills ◽  
Loop Approximation ◽  
Feynman Rules

A composite non-abelian model SU(N) × SU(N) is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by SU(N) × SU(N). The corresponding Feynman rules of the model are studied. Propagators and vertices are derived in the momentum space. As physical application, instead of considering the color symmetry SUc(3) for QCD, we substitute it by the combination SUc(3) × SUc(3). It yields a possibility to go beyond QCD symmetry in the sense that quarks are preserved with three colors. This extension provides composite quarks in triplets and sextets multiplets accomplished with the usual massless gluons plus massive gluons. We present a power counting analysis that satisfies the renormalization conditions as well as one studies the structure of radiative corrections to one loop approximation. Unitary condition is verified at tree level. Tachyons are avoided. For end, one extracts a BRST symmetry from lagrangian and Slavnov-Tayloridentities.

scholarly journals Simplicity of AdS supergravity at one loop

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Luis F. Alday ◽  
Xinan Zhou
Keyword(s):  
Closed Form ◽  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Loop Level ◽  
Level Data ◽  
Space Limit ◽  
Loop Amplitude

Abstract We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ O 2 SG O 2 SG O p SG O p SG correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

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