Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-01-04
Theor. Math. Phys, 169(3), (2011) 1704-1723
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, based on talks at Integrable Systems in Quantum Theory, Leiden, April 2010, Workshop on Combinatorics of Moduli spac
Scientific paper
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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