A proposal for nonabelian mirrors

Understand

In this paper we propose a systematic construction of mirrors of nonabelian two dimensional (2,2) supersymmetric gauge theories.

• Specifically, we propose a construction of B-twisted Landau-Ginzburg orbifolds whose correlation functions match those of A-twisted supersymmetric gauge theories, and whose critical loci reproduce quantum cohomology and Coulomb branch relations in A-twisted gauge theories, generalizing the Hori-Vafa mirror construction.
• We check this proposal in a wide variety of examples.
• For instance, we construct mirrors corresponding to Grassmannians and two-step flag manifolds, as well as complete intersections therein, and explicitly check predictions for correlation functions and quantum cohomology rings, as well as other properties.