# 3d N=4 Bootstrap and Mirror Symmetry

### Submission summary

 As Contributors: Chi-Ming Chang · Ying-Hsuan Lin Preprint link: scipost_202102_00025v1 Date submitted: 2021-02-17 15:22 Submitted by: Chang, Chi-Ming Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approaches: Theoretical, Computational

### 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.

###### Current status:
Editor-in-charge assigned

We thank the referee for the comments., and we have made corrections and adjustments accordingly, please see our new version. Our responses are below.

1- Please see the footnote 30 on page 56 of the new version. 2- Please see the footnote 25 on page 43 and the footnote 28 on page 48 of the new version. 3- We added a brief summary of the main results of this paper in the introduction section of the new version.

### List of changes

1- A summary of the main results has been added in the introduction section.
2- Footnote 25 on page 43, footnote 28 on page 48, and footnote 30 on page 56 have been added.
3- The notation for the flavor central charge is changed, for example in (2.7) on page 8.