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Journal of High Energy Physics

, 2012:132 | Cite as

Matrix models for supersymmetric Chern-Simons theories with an ADE classification

  • Daniel R. Gulotta
  • J. P. Ang
  • Christopher P. HerzogEmail author
Article

Abstract

We consider \( \mathcal{N} \) = 3 supersymmetric Chern-Simons (CS) theories that contain product U(N ) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these theories on an S 3 in the large N limit. We show that the only such CS theories for which the long range forces between the eigenvalues cancel have quivers which are in one-to-one correspondence with the simply laced affine Dynkin diagrams. As the A n series was studied in detail before, in this paper we compute the partition function for the D 4 quiver. The D 4 example gives further evidence for a conjecture that the saddle point eigenvalue distribution is determined by the distribution of gauge invariant chiral operators. We also see that the partition function is invariant under a generalized Seiberg duality for CS theories.

Keywords

AdS-CFT Correspondence Chern-Simons Theories Duality in Gauge Field Theories 1/N Expansion 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Daniel R. Gulotta
    • 1
  • J. P. Ang
    • 1
  • Christopher P. Herzog
    • 1
    Email author
  1. 1.Department of PhysicsPrinceton UniversityPrincetonU.S.A

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