Strong coupling dynamics of four-dimensional $N = 1$ gauge theories from M-theory fivebrane

It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N = 2 supersymmetric gauge theories in four dimensions. We follow the recent M-theory description by Witten and show that it can be used to study theories with N = 1 supersymmetry. The N = 2 supersymmetry can be broken to N = 1 by turning on a mass for the adjoint chiral superfield in the N -2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N -1 theory with SU(N C ) gauge group and Nf quarks. For N c > Nf, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For -Nc < Nf, we study the deformation space of the brane configuration and compare it with the moduli space of the N = 1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N c = Nf. We also prove the type II s-rule in M-theory and find new non-renormalization theorems for N -1 superpotentials.