More nonabelian mirrors and some two-dimensional dualities

TL;DR

Gu, Parsian, and Sharpe extend the nonabelian mirror construction from connected gauge groups to $O_{ obreak\pm}(k)$ with discrete theta angles, modeling mirrors as Landau-Ginzburg orbifolds with additional ${\mathbb Z}_2$ twists to capture fixed-point effects. They test the proposal across a network of 2D dualities relating $SO$ and $O$ theories by carefully counting vacua in the mirrors, including contributions from twisted sectors, and by matching central charges in IR SCFTs where applicable. The results show that vacuum structures and central charges align with the expected IR dualities, providing strong evidence that the extended mirror construction correctly captures nontrivial nonabelian dualities involving nonconnected groups. The work broadens the applicability of nonabelian mirrors and highlights how orbifold twisted sectors encode deep IR dualities in two dimensions.

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.