Free Energy of the Two-Matrix Model/dToda Tau-Function

Details Free Energy of the Two-Matrix Model/dToda Tau-Function Free Energy of the Two-Matrix Model/dToda Tau-Function

2003-06-19

arxiv.org/abs/hep-th/0306184v5

Nucl.Phys.B669:435-461,2003

Physics

High Energy Physics

High Energy Physics - Theory

Ver 2: 18 pages added important formulas for higher genus spectral curves, few typos removed (and few added). Ver 3: 19 pages

Scientific paper

10.1016/j.nuclphysb.2003.07.029

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.

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