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 τ-function of the dispersionless two-dimensional Toda hierarchy. The formula generalizes the case of conformal maps of Jordan curves studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.
Free energy of the two-matrix model/dToda tau-function / Bertola, M.. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 669:3(2003), pp. 435-461. [10.1016/j.nuclphysb.2003.07.029]
Free energy of the two-matrix model/dToda tau-function
Bertola, M.
2003-01-01
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 τ-function of the dispersionless two-dimensional Toda hierarchy. The formula generalizes the case of conformal maps of Jordan curves studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan. Finally we generalize the formula found in genus zero to the case of spectral curves of arbitrary genus with certain fixed data.| File | Dimensione | Formato | |
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