6D (2,0) Bootstrap with soft-Actor-Critic

TL;DR

This paper applies the soft-Actor-Critic algorithm to numerically study the 6D (2,0) superconformal bootstrap, deriving bounds on CFT data and conjecturing connections to known theories, while also releasing a new computational tool.

Contribution

It introduces a novel application of SAC to the 6D (2,0) bootstrap and provides a new Python package for this purpose, advancing numerical methods in superconformal theories.

Findings

Derived two curves for 80 CFT data points related to (2,0) theories

Achieved results competitive with existing bootstrap bounds

Conjectured correspondence with A- and D-series (2,0) theories

Abstract

We study numerically the 6D (2,0) superconformal bootstrap using the soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the four-point functions of scalar superconformal primaries in the energy-momentum multiplet. Starting from the supergravity limit, we perform searches for adiabatically varied central charges and derive two curves for a collection of 80 CFT data (70 of these data correspond to unprotected long multiplets and 10 to protected short multiplets). We conjecture that the two curves capture the A- and D-series (2,0) theories. Our results are competitive when compared to the existing bounds coming from standard numerical bootstrap methods, and data obtained using the OPE inversion formula. With this paper we are also releasing our Python implementation of the SAC algorithm, BootSTOP. The paper discusses the main functionality features of this package.