On Gauge Theories as Matrix Models
Abstract
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition functions of supersymmetric gauge theories. The exact quasiclassical solution for the case of conformal four-dimensional theory is studied in detail, and some aspects of its relation with the recently proposed logarithmic beta-ensembles are considered. We discuss also the "quantization" of this picture in terms of two-dimensional conformal theory with extended symmetry, and stress its difference from common picture of perturbative expansion a la matrix models. Instead, the representation for Nekrasov functions in terms of conformal blocks or Whittaker vector suggests some nontrivial relation with Teichmueller spaces and quantum integrable systems.
Cite
@article{arxiv.1101.0676,
title = {On Gauge Theories as Matrix Models},
author = {A. Marshakov},
journal= {arXiv preprint arXiv:1101.0676},
year = {2012}
}
Comments
26 pages, based on talks at Integrable Systems in Quantum Theory, Leiden, April 2010, Workshop on Combinatorics of Moduli space, Moscow, May 2010, Synthesis of Integrabilities in the Context of Gauge/String Duality, Moscow, September 2010 and Geometry and Integrable Systems, Moscow, December 2010