Supersymmetric Gauge Theories with Classical Groups via M Theory Fivebrane

TL;DR

This paper uses M theory fivebrane configurations to analyze the moduli space, Higgs branches, and vacuum structure of N=1 and N=2 supersymmetric gauge theories with classical groups, providing geometric insights and matching field theory results.

Contribution

It constructs explicit fivebrane configurations for classical gauge groups, elucidates Higgs branches, and confirms field theory vacua through geometric methods.

Findings

Higgs branches are interpreted via fivebrane configurations.

Constructed fivebrane configurations for special Higgs branch roots.

Matched monopole condensations and meson VEVs with field theory predictions.

Abstract

We study the moduli space of vacua of four dimensional N=1 and N=2 supersymmetric gauge theories with the gauge groups $Sp(2 N_c)$, $SO(2 N_c)$ and $SO(2 N_c +1)$ using the M theory fivebrane. Higgs branches of the N=2 supersymmetric gauge theories are interpreted in terms of the M theory fivebrane and the type IIA $s$-rule is realized in it. In particular we construct the fivebrane configuration which corresponds to a special Higgs branch root. This root is analogous to the baryonic branch root in the $SU(N_c)$ theory which remains as a vacuum after the adjoint mass perturbation to break N=2 to N=1. Furthermore we obtain the monopole condensations and the meson vacuum expectation values in the confining phase of N=1 supersymmetric gauge theories using the fivebrane technique. These are in complete agreement with the field theory results for the vacua in the phase with a single confined photon.