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Journal of High Energy Physics

, 2010:22 | Cite as

Penner type matrix model and Seiberg-Witten theory

  • Tohru EguchiEmail author
  • Kazunobu Maruyoshi
Article

Abstract

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of N f = 4, \( \mathcal{N} \) = 2 supersymmetric gauge theory being related as q UV = ϑ2(q IR)43(q IR)4. We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve.

We also discuss the decoupling of massive flavors from the N f = 4 matrix model and derive matrix models describing asymptotically free \( \mathcal{N} \) = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of \( \mathcal{N} \) = 2 supersymmetric gauge theories.

Keywords

Matrix Models Extended Supersymmetry Supersymmetric gauge theory Duality in Gauge Field Theories 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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