This article is cited in 3 papers

Gauge theories as matrix models

A. V. Marshakov<sup>ab

a</sup> Lebedev Physical Institute, RAS, Moscow, Russia
^b Institute of Theoretical and Experimental Physics, Moscow, Russia

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.

Keywords: supersymmetric gauge theory, matrix model, two-dimensional conformal field theory, highest-weight module of the Virasoro algebra.

Received: 05.03.2011

DOI: 10.4213/tmf6737

 English version: Theoretical and Mathematical Physics, 2011, 169:3, 1704–1723

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