Aspects of superconformal field theories in six dimensions

TL;DR

This paper develops an analytic superspace formalism for six-dimensional superconformal theories, solves Ward identities for four-point functions, and performs a detailed conformal partial wave analysis including free and AdS dual theories.

Contribution

It introduces a new formalism for 6D superconformal theories, explicitly solves Ward identities, and analyzes four-point functions using Schur and Jack polynomials.

Findings

Explicit solutions for four-point functions in 6D superconformal theories.

Conformal partial wave expansion for free and AdS dual four-point functions.

Identification of operators at the unitarity bound with potential non-anomalous dimensions.

Abstract

We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve them. We then consider the four-point function of four energy momentum multiplets in detail, explicitly solving the Ward identities in this case. We expand the four-point function using both Schur polynomials, which lead to a simple formula in terms of a single function of two variables, and (a supersymmetric generalisation of) Jack polynomials, which allow a conformal partial wave expansion. We then perform a complete conformal partial wave analysis of both the free theory four-point function and the AdS dual four-point function. We also discuss certain operators at the threshold of the series a) unitary bound, and prove that some such operators may not develop anomalous dimensions, by finding selection rules for certain three-point functions. For those operators which are not protected, we find representations with which they may combine to become long.