Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble

Details Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble

2011-03-28

arxiv.org/abs/1103.5470v2

Theor.Math.Phys.171 (2012) 505-522; Teor.Mat.Fiz.171 (2012) 96-115

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

The exact free energy of matrix model always obeys the Seiberg-Witten (SW) equations on a complex curve defined by singularities of the quasiclassical resolvent. The role of SW differential is played by the exact one-point resolvent. We show that these properties are preserved in generalization of matrix models to beta-ensembles. However, since the integrability and Harer-Zagier topological recursion are still unavailable for beta-ensembles, we need to rely upon the ordinary AMM/EO recursion to evaluate the first terms of the genus expansion. Consideration in this paper is restricted to the Gaussian model.

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