A proposal for nonabelian mirrors in two-dimensional theories
In this talk we will describe a proposal for nonabelian mirrors to two-dimensional (2,2) supersymmetric
gauge theories, generalizing the Hori-Vafa construction for abelian gauge theories. Specifically, we will describe a construction of B-twisted Landau-Ginzburg orbifolds whose classical physics encodes Coulomb branch relations (quantum cohomology), excluded loci, and correlation functions of A-twisted gauge theories. The proposal has been checked in a wide variety of cases, but the talk will focus on exploring the proposal in two examples: Grassmannians (constructed as U(k) gauge theories with fundamental matter), and SO(2k) gauge theories. If time permits, we will also discuss how this mirror proposal can be applied to test and refine recent predictions for IR behavior of pure supersymmetric SU(n) gauge theories in two dimensions.