N=4 super-Yang-Mills in LHC superspace. Part II: Non-chiral correlation functions of the stress-tensor multiplet

TL;DR

This paper develops supergraph Feynman rules for non-chiral stress-tensor multiplet correlators in N=4 super-Yang-Mills theory, revealing a simple Grassmann shift relation to chiral correlators within the LHC superspace framework.

Contribution

It introduces a novel method to compute non-chiral correlators using a Grassmann shift from chiral correlators in LHC superspace, applicable at Born level.

Findings

Feynman rules derived from chiral correlators via Grassmann shift

Method applicable to various supermultiplets including BPS and Konishi

Analysis performed in the self-dual sector of the theory

Abstract

We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.