Gauge theories as matrix models

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Abstract

We discuss the relation between the Seiberg-Witten prepotentials, Nekrasov functions, and matrix models. On the semiclassical level, we show that the matrix models of Eguchi-Yang type are described by instantonic contributions to the deformed partition functions of supersymmetric gauge theories. We study the constructed explicit exact solution of the four-dimensional conformal theory in detail and also discuss some aspects of its relation to the recently proposed logarithmic beta-ensembles. We also consider "quantizing" this picture in terms of two-dimensional conformal theory with extended symmetry and stress its difference from the well-known picture of the perturbative expansion in matrix models. Instead, the representation of Nekrasov functions using conformal blocks or Whittaker vectors provides a nontrivial relation to Teichmüller spaces and quantum integrable systems.

Original languageEnglish
Pages (from-to)1704-1723
Number of pages20
JournalTheoretical and Mathematical Physics
Volume169
Issue number3
DOIs
Publication statusPublished - Dec 2011
Externally publishedYes

Keywords

  • highest-weight module of the Virasoro algebra
  • matrix model
  • supersymmetric gauge theory
  • two-dimensional conformal field theory

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