N=4 superconformal Ward identities for correlation functions
A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatchev
TL;DR
The authors develop a symmetry-driven method to determine the four-point correlator of the ${\cal N}=4$ energy-momentum supermultiplet, obtaining a compact expression that is fixed by a unique fermionic invariant and a single function $\Phi(u,v)$ of cross-ratios. They disentangle rational (Born) and anomalous contributions, construct the full anomalous piece via a nilpotent, abelian fermionic algebra, and match to the lowest component to fix the bosonic function. The framework yields explicit component correlators for currents and the energy-momentum tensor, and it provides a detailed treatment of charge-flow (event-shape) correlations, uncovering universal relations across different flow channels that follow from the underlying superconformal symmetry. The results offer a dynamics-free, broadly applicable toolkit for analyzing four-point functions and flow observables in ${\cal N}=4$ superconformal theories, with potential insights for bootstrap analyses and QCD-like observables.
Abstract
In this paper we study the four-point correlation function of the energy-momentum supermultiplet in theories with N=4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N=4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N=4 super Yang-Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.