Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and thechiral ring structure in a supersymmetric U(N) gauge theory with an adjointchiral superfield and an arbitrary superpotential. A certain generalization ofthe Konishi anomaly leads to an equation which is identical to the loopequation of a bosonic matrix model. This allows us to solve for the expectationvalues of the chiral operators as functions of a finite number of ``integrationconstants.'' From this, we can derive the Dijkgraaf-Vafa relation of theeffective superpotential to a matrix model. Some of our results are applicableto more general theories. For example, we determine the classical relations andquantum deformations of the chiral ring of $\N=1$ super Yang-Mills theory withSU(N) gauge group, showing, as one consequence, that all supersymmetric vacuaof this theory have a nonzero chiral condensate.Comment: 67 pages, minor change