Supersymmetric gauge theories with classical groups via M theory fivebrane

Abstract

We study the moduli space of vacua of four-dimensional N = 1and 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.