Strong Coupling Dynamics of Four-Dimensional N=1 Gauge Theories from M Theory Fivebrane

TL;DR

This paper uses M theory fivebrane configurations to analyze the strong coupling dynamics of four-dimensional N=1 supersymmetric gauge theories, extending previous IIA fivebrane methods from N=2 to N=1 cases.

Contribution

It demonstrates how M theory fivebrane setups can be used to study N=1 gauge theories, including superpotential encoding and moduli space deformations, with results matching field theory predictions.

Findings

Encoding of Affleck-Dine-Seiberg superpotential in brane configurations

Agreement of brane moduli space with quantum deformations

Proof of type II s-rule and new non-renormalization theorems

Abstract

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 N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, 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 = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.