On Four-Point Functions of Half-BPS Operators in General Dimensions

TL;DR

This paper derives and solves superconformal Ward identities for four-point functions of half-BPS operators across various dimensions, revealing a universal structure parameterized by arbitrary functions, with special features in four dimensions.

Contribution

It provides a universal framework for four-point functions of half-BPS operators in multiple dimensions using harmonic superspace and Jack polynomial expansions, including solutions and operator product expansion insights.

Findings

General solution parameterized by two-variable functions

Special case in four dimensions with additional single-variable functions

Connection to conformal partial wave amplitudes in arbitrary dimensions

Abstract

We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.