The $(2,0)$ superconformal bootstrap

TL;DR

This paper develops the conformal bootstrap approach for six-dimensional $(2,0)$ superconformal field theories, providing bounds on operator dimensions and OPE coefficients, and presents evidence that the $A_1$ theory uniquely saturates the minimal central charge.

Contribution

It introduces the superconformal bootstrap for 6d $(2,0)$ theories, deriving bounds and analytic results, and identifies the $A_1$ theory as the minimal central charge solution.

Findings

The $A_1$ theory has the minimal central charge $c=25$ among $(2,0)$ theories.

Bounds on operator dimensions and OPE coefficients are derived and match holographic predictions at large $c$.

The stress tensor four-point function of the $A_1$ theory is the unique solution at $c=25$.

Abstract

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.