More non-Abelian mirrors and some two-dimensional dualities

In this paper, we extend the non-Abelian 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 the 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 the twisted sector contributions. This is a technical novelty relative to the 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 the central charges computed from the Landau-Ginzburg mirrors match those expected for the IR SCFTs.