Generalized matrix models and AGT correspondence at all genera

  • Giulio Bonelli
  • Kazunobu Maruyoshi
  • Alessandro Tanzini
  • Futoshi Yagi
Open Access
Article

Abstract

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional \( \mathcal{N} = 2 \) SU(2)n+3g−3 gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the \( \mathcal{N} = 2 \) gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.

Keywords

Supersymmetric gauge theory Matrix Models Extended Supersymmetry Conformal and W Symmetry 

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© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Giulio Bonelli
    • 1
  • Kazunobu Maruyoshi
    • 1
  • Alessandro Tanzini
    • 1
  • Futoshi Yagi
    • 2
  1. 1.International School of Advanced Studies (SISSA) and INFN, Sezione di TriesteTriesteItaly
  2. 2.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance

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