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- Title
Resolvents and Seiberg-Witten representation for a Gaussian β-ensemble.
- Authors
Mironov, A.; Morozov, A.; Popolitov, A.; Shakirov, Sh.
- Abstract
The exact free energy of a matrix model always satisfies the Seiberg-Witten equations on a complex curve defined by singularities of the semiclassical resolvent. The role of the Seiberg-Witten differential is played by the exact one-point resolvent in this case. We show that these properties are preserved in the generalization of matrix models to β-ensembles. But because the integrability and Harer-Zagier topological recursion are still unavailable for β-ensembles, we must rely on the ordinary Alexandrov-Mironov-Morozov/Eynard-Orantin recursion to evaluate the first terms of the genus expansion. We restrict our consideration to the Gaussian model.
- Subjects
GIBBS' free energy; MATHEMATICAL models; SEIBERG-Witten invariants; RECURSION theory; GAUSSIAN processes; MATHEMATICAL analysis
- Publication
Theoretical & Mathematical Physics, 2012, Vol 171, Issue 1, p505
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1007/s11232-012-0049-y