## 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.

Original language | English (US) |
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Pages (from-to) | 1611-1666 |

Number of pages | 56 |

Journal | Journal of High Energy Physics |

Volume | 6 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- 1/N Expansion
- Duality in Gauge Field Theories
- Supersymmetric Effective Theories
- Supersymmetry and Duality