Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM

By B. Eden, P. Heslop, G. Korchemsky, E. Sokatchev. 2011

154 citations recorded by the source corpus.

Abstract We study the four-point correlation function of stress-tensor supermultiplets in N = 4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N = 4 superconformal symmetry, the resulting all-loop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the three-loop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the three-loop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the three-loop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the three-point function of two half-BPS operators and one Konishi operator at three-loop level. We use the same technique to work out a compact form for the four-loop four-point integrand and discuss the generalisation to higher loops.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/cdfde94af5fa901ade83d164c8a656e9a197beba

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Citations in the corpus

Hexagonalization of correlation functions (2016, unknown): “J H E P 0 1 ( 2 0 1 7 ) 1 3 0 appear at three loops [32].”
From correlation functions to event shapes (2013, background): “8) is known explicitly in terms of functions with known Mellin representation up to two loops [58, 53, 59, 60], and up to six loops in terms of basis integrals [56], which were successfully computed at three-loop order [61].”
Conformal Regge theory (2012, methodology): “In particular, it would be interesting to study the Regge limit of the four-point function〈 Tr(XZ)(x1) Tr ( XZ ) (x2) Tr ( Y Z ) (x3) Tr ( Y Z ) (x4) 〉 , (114) where X, Y and Z are complex scalar fields of SYM.”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, unknown): “As was shown in [48, 49], the consistency of (2.”