Free Energy of the Two-Matrix Model/dToda Tau-Function
Abstract
We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal maps of Jordan curves. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.
Cite
@article{arxiv.hep-th/0306184,
title = {Free Energy of the Two-Matrix Model/dToda Tau-Function},
author = {M. Bertola},
journal= {arXiv preprint arXiv:hep-th/0306184},
year = {2009}
}
Comments
Ver 2: 18 pages added important formulas for higher genus spectral curves, few typos removed (and few added). Ver 3: 19 pages (minor changes). Typos removed, added appendix and improved exposition Ver 4: 19 pages, minor corrections. Version submitted Ver 4; corrections prompted by referee and accepted in Nuclear Phys. B