# 3d N=4 Bootstrap and Mirror Symmetry

### Submission summary

 As Contributors: Chi-Ming Chang · Ying-Hsuan Lin Preprint link: scipost_202102_00025v2 Date accepted: 2021-04-16 Date submitted: 2021-04-03 09:38 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:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

We have added the reference suggested by the referee.

### List of changes

Added reference 98 on page 57.

### Submission & Refereeing History

Resubmission scipost_202102_00025v2 on 3 April 2021
Resubmission scipost_202102_00025v1 on 17 February 2021
Submission 1910.03600v2 on 21 October 2020