Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Details Chiral Rings and Anomalies in Supersymmetric Gauge Theory Chiral Rings and Anomalies in Supersymmetric Gauge Theory

2002-11-18

arxiv.org/abs/hep-th/0211170v2

JHEP 0212:071,2002

Physics

High Energy Physics

High Energy Physics - Theory

67 pages, minor changes

Scientific paper

10.1088/1126-6708/2002/12/071

Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of $\N=1$ super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.

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