## 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 language | English |
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Pages (from-to) | 1704-1723 |

Number of pages | 20 |

Journal | Theoretical and Mathematical Physics |

Volume | 169 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 2011 |

Externally published | Yes |

## Keywords

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