Friday, February 3, 2012

1101.0676 (A. Marshakov)

On Gauge Theories as Matrix Models    [PDF]

A. Marshakov
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.
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