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2011

Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble

Mironov, A., Morozov, A., Popolitov, A. et al.

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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.

Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble · Around

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2009

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