Two-dimensional supersymmetric gauge theories with exceptional gauge groups

TL;DR

This work extends the Gu-Sharpe nonabelian mirror construction to 2d (2,2) gauge theories with exceptional groups $G_2$, $F_4$, $E_6$, $E_7$, and $E_8$, constructing explicit mirror Landau-Ginzburg orbifolds and deriving the corresponding Coulomb/quantum cohomology relations and excluded loci. Across all cases, the authors analyze Weyl-group actions, compute vacuum structures for various numbers of fundamental flavors, and verify IR behavior of pure gauge theories, finding evidence that pure simply-connected semisimple groups flow in the IR to a free theory of as many twisted chiral multiplets as the rank of the group. The results illuminate how weight-lattice conventions and theta-angle periodicities affect mirror data, and show precise agreement with A-model computations after appropriate basis choices and rescalings. Overall, the paper provides a comprehensive framework for understanding mirrors of exceptional 2d gauge theories and the IR fate of pure exceptional groups, with potential implications for dualities and quantum cohomology in nonabelian settings.

Abstract

We apply the recent proposal for mirrors of nonabelian (2,2) supersymmetric two-dimensional gauge theories to make predictions for two-dimensional supersymmetric gauge theories with exceptional gauge groups G2, F4, E6, E7, and E8. We compute the mirror Landau-Ginzburg models and predict excluded Coulomb loci and Coulomb branch relations (quantum cohomology). We also discuss the relationship between weight lattice normalizations and theta angle periodicities in the proposal, and explore different conventions for the mirrors. Finally, we discuss the behavior of pure gauge theories with exceptional gauge groups under RG flow, and describe evidence that any pure supersymmetric two-dimensional gauge theory with connected and simply-connected semisimple gauge group flows in the IR to a free theory of as many twisted chiral superfields as the rank of the gauge group, extending previous results for SU, SO, and Sp gauge theories.

Figures (2)

• Figure 1: Roots of $G_2$.
• Figure 2: Weights of ${\bf 7}$ of $G_2$.