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arXiv · hep-th/0211170

Chiral Rings and Anomalies in Supersymmetric Gauge Theory

Freddy Cachazo·Michael R. Douglas·Nathan Seiberg·Edward Witten
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Abstract

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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Freddy Cachazo, Michael R. Douglas, Nathan Seiberg, Edward Witten. 2002-12-17. Chiral Rings and Anomalies in Supersymmetric Gauge Theory. https://doi.org/10.1088/1126-6708%2F2002%2F12%2F071

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