Supersymmetric Gauge Theories with Classical Groups via M Theory Fivebrane

We study the moduli space of vacua of four dimensional N = 1 and N = 2 supersymmetric gauge theories with the gauge groups Sp(2Nc), SO(2Nc) and SO(2Nc + 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(Nc) 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.