Chiral rings and anomalies in supersymmetric gauge theory

Freddy Cachazo, Michael R. Douglas, Nathan Seiberg, Edward Witten

Research output: Contribution to journalArticlepeer-review

278 Scopus citations


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 languageEnglish (US)
Pages (from-to)1611-1666
Number of pages56
JournalJournal of High Energy Physics
Issue number12
StatePublished - Dec 1 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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


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