# More nonabelian mirrors and some two-dimensional dualities

## TL;DR

This paper extends nonabelian mirror symmetry to O(k) gauge theories with discrete theta angles, analyzing vacua and dualities through Landau-Ginzburg orbifolds and confirming IR properties.

## Contribution

It introduces a novel extension of nonabelian mirror proposals to O(k) gauge groups with discrete theta angles, incorporating twisted sector contributions.

## Key findings

- Successfully counts and compares vacua in mirror theories
- Confirms IR central charges match expected SCFT values
- Identifies technical challenges with orbifold fixed points

## Abstract

In this paper we extend the nonabelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of O(k) gauge groups with discrete theta angles. We check our proposed extension by counting and comparing vacua in mirrors to known dual two-dimensional (S)O(k) gauge theories. The mirrors in question are Landau-Ginzburg orbifolds, and for mirrors to O(k) gauge theories, the critical loci of the mirror superpotential often intersect fixed-point loci, so that to count vacua, one must take into account twisted sector contributions. This is a technical novelty relative to mirrors of gauge theories with connected gauge groups, for which critical loci do not intersect fixed-point loci and so no orbifold twisted sector contributions are pertinent. The vacuum computations turn out to be a rather intricate test of the proposed mirrors, in particular as untwisted sector states in the mirror to one theory are often exchanged with twisted sector states in the mirror to the dual. In cases with nontrivial IR limits, we also check that central charges computed from the Landau-Ginzburg mirrors match those expected for the IR SCFTs.