Gauge theories as matrix models |
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Authors: | A V Marshakov |
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Institution: | 1.Tamm Theory Department, Lebedev Physical Institute,RAS,Moscow,Russia;2.Institute of Theoretical and Experimental Physics,Moscow,Russia |
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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. |
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