3d N=4 Bootstrap and Mirror Symmetry

TL;DR

This paper combines conformal bootstrap and supersymmetric localization to study 3d N=4 superconformal field theories, revealing new constraints on operator product expansion data and exploring mirror symmetry effects.

Contribution

It introduces a novel approach integrating bootstrap and localization methods to analyze 3d N=4 SCFTs, including the impact of mirror symmetry and TQM sectors.

Findings

Exact central charges from localization.

Universal bootstrap bounds on OPE data.

Identification of self-mirror theory saturating bounds.

Abstract

We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$ theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with $SU(2) \times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry thereof.