Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 1

Two-dimensional supersymmetric gauge theories with exceptional gauge groups

Pages: 67 – 123

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n1.a3

Authors

Zhuo Chen (Department of Physics, Virginia Polytechnic Institute, Blacksburg, Va., U.S.A.)

Wei Gu (Department of Physics, Virginia Polytechnic Institute, Blacksburg, Va., U.S.A.)

Hadi Parsian (Department of Physics, Virginia Polytechnic Institute, Blacksburg, Va., U.S.A.)

Eric Sharpe (Department of Physics, Virginia Polytechnic Institute, Blacksburg, Va., U.S.A.)

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 $G_2$, $F_4$, $E_6$, $E_7$, and $E_8$. 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 $S_p$ gauge theories.

Published 22 May 2020