20′ five-point function from AdS5× S5 supergravity

140

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams -we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams -in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.

Section: Discussionmentioning

confidence: 99%

Unitarity methods in AdS/CFT

Meltzer

Perlmutter

Sivaramakrishnan

2020

140

“…The correlation functions of length-two half-BPS operators (also known as 20 operators) in N = 4 SYM have been studied extensively in the literature both at weak [1][2][3][4][5] and strong coupling [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. It is well known that the two-and three-point functions of those operators are protected by supersymmetry [7,20] while higher-point functions receive non-trivial corrections.…”

Section: Introductionmentioning

confidence: 99%

Non-planar data of $$ \mathcal{N} $$ = 4 SYM

Fleury

Pereira

2020

Self Cite

The four-point function of length-two half-BPS operators in N = 4 SYM receives nonplanar corrections starting at four loops. Previous work relied on the analysis of symmetries and logarithmic divergences to fix the integrand up to four constants. In this work, we compute those undetermined coefficients and fix the integrand completely by using the reformulation of N = 4 SYM in twistor space. The final integrand can be written as a combination of finite conformal integrals and we have used the method of asymptotic expansions to extract non-planar anomalous dimensions and structure constants for twist-two operators up to spin eight. Some of the results were already know in the literature and we have found agreement with them.

“…give non trivial predictions at twist 4 and twist 6 12. Recall that there are two double trace operators in R 6,l,[000] , therefore the twist…”

mentioning

confidence: 99%

One-loop amplitudes in AdS5×S5 supergravity from $$ \mathcal{N} $$ = 4 SYM at strong coupling

Aprile

Drummond

Heslop

et al. 2020

171

We explore the structure of maximally supersymmetric Yang-Mills correlators in the supergravity regime. We develop an algorithm to construct one-loop supergravity amplitudes of four arbitrary Kaluza-Klein supergravity states, properly dualised into single-particle operators. We illustrate this algorithm by constructing new explicit results for multi-channel correlation functions, and we show that correlators which are degenerate at tree level become distinguishable at one-loop. The algorithm contains a number of subtle features which have not appeared until now. In particular, we address the presence of non-trivial low twist protected operators in the OPE that are crucial for obtaining the correct oneloop results. Finally, we outline how the differential operators D pqrs and ∆ (8) , which play a role in the context of the hidden 10d conformal symmetry at tree level, can be used to reorganise our one-loop correlators.