3d N = 4 Bootstrap and Mirror Symmetry

We investigate the non-BPS realm of 3d N = 4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d 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 Z(2) mirror action for the SCFT singleand 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) x SU(2) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z(2) symmetry thereof.

Automated summary

The non-BPS realm of 3d N = 4 superconformal field theory is investigated by combining the non-perturbative methods of the conformal bootstrap and supersymmetric localization, utilizing special features such as mirror symmetry and topological quantum mechanics. Numerical bootstrap is applied to obtain universal constraints on OPE data, with a key factor being the determination of mixed-branch superconformal blocks. The simplest known self-mirror theory with SU(2) x SU(2) flavor symmetry satisfies bootstrap bounds, enabling extraction of non-BPS data and examination of its self-mirror Z(2) symmetry.