All three-loop four-point correlators of half-BPS operators in planar N $$ \mathcal{N} $$ = 4 SYM

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.

Section: Resultsmentioning

confidence: 99%

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

Fleury

Pereira

2020

“…The particular class of single-valued polylogarithms of interest here are linear combinations of polylogarithms constructed on the singularities (or 'letters') {x, 1 − x,x, 1 −x} such that they are single-valued whenx is taken to be the complex conjugate of x. They are constructed in general in [50] and appear in many contexts to discuss the perturbative contributions to the correlation functions p 1 p 2 p 3 p 4 [40,42] as well as in multi-Regge kinematics of scattering amplitudes [51,52] and Feynman integral calculations [53,54]. Since our result for the double discontinuity F…”

Section: Completion To a Crossing Symmetric Amplitudementioning

confidence: 99%

Quantum gravity from conformal field theory

Aprile

Drummond

Heslop

et al. 2018

166

392

We bootstrap loop corrections to AdS 5 supergravity amplitudes by enforcing the consistency of the known classical results with the operator product expansion of N = 4 super Yang-Mills theory. In particular this yields much new information on the spectrum of double-trace operators which can then be used, in combination with superconformal symmetry and crossing symmetry, to obtain a prediction for the one-loop amplitude for four graviton multiplets in AdS. This in turn yields further new results on subleading O(1/N 4 ) corrections to certain double-trace anomalous dimensions.

“…long (27) Note that the YT representation of a long multiplet is invariant up to the shift-symmetry,…”

Section: Review Of the Scpw Expansionmentioning

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.