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The ABCDEF’s of matrix models for supersymmetric Chern-Simons theories

  • Daniel R. Gulotta
  • Christopher P. Herzog
  • Tatsuma NishiokaEmail author
Article

Abstract

We consider \( \mathcal{N} = {3} \) supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S 3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a \( {{\mathbb{Z}}_{{2}}} \) outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.

Keywords

Matrix Models 1/N Expansion 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Daniel R. Gulotta
    • 1
  • Christopher P. Herzog
    • 2
  • Tatsuma Nishioka
    • 1
    Email author
  1. 1.Department of PhysicsPrinceton UniversityPrincetonU.S.A.
  2. 2.YITP, Stony Brook UniversityStony BrookU.S.A.

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