M theory fivebrane and SQCD

A low energy effective theory of parallel D(irichlet) branes is a gauge theory with sixteen supercharges, but one can consider a web of brane to realize situations with reduced number of supersymmetry [1]. In this talk, I will discuss four-dimensional theories with N = 1 and 2 supersymmetry (i.e. four and eight supercharges). In the case of theories with N = 2 supersymmetry, the exact description of the Coulomb branch is given by reinterpreting the web of branes as a configuration of a single fivebrane in the IIA theory [2,3]. Recently we studied the case with N = 1 supersymmetry, and found that description in term of the fivebrane in M Theory captures strong coupling dynamics of the N = 1 gauge theory in four dimensions [4]. In particular, we found that the configuration of the fivebrane geometrically encodes information on the Affleck-Dine-Seiberg superpotential and the structure of the quantum moduli space of vacua. Simultaneously to our work, the case without matter field was studied in [5]. A related work also appeared in [6].