Implications of Superconformal Symmetry for Interacting (2,0) Tensor Multiplets

TL;DR

This paper explores the structure of four-point functions in six-dimensional (2,0) superconformal theories, deriving solutions from Ward identities, computing amplitudes via supergravity, and confirming non-renormalization properties.

Contribution

It provides a detailed analysis of four-point correlators in (2,0) theories, linking superconformal symmetry, group theory, and supergravity computations to reveal new structural insights.

Findings

Solution of Ward identities expressed in terms of a single prepotential

Supergravity calculations match the conformal partial wave expansion

Leading OPE terms agree with non-renormalization theorems

Abstract

We study the structure of the four-point correlation function of the lowest-dimension 1/2 BPS operators (stress-tensor multiplets) in the (2,0) six-dimensional theory. We first discuss the superconformal Ward identities and the group-theoretical restrictions on the corresponding OPE. We show that the general solution of the Ward identities is expressed in terms of a single function of the two conformal cross-ratios ("prepotential"). Using the maximally extended gauged seven-dimensional supergravity, we then compute the four-point amplitude in the supergravity approximation and identify the corresponding prepotential. We analyze the leading terms in the OPE by performing a conformal partial wave expansion and show that they are in agreement with the non-renormalization theorems following from representation theory. The investigation of the (2,0) theory is carried out in close parallel with the familiar four-dimensional N=4 super-Yang-Mills theory.