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$1/N^2$ correction to free energy in hermitian two-matrix model

B. Eynard·A. Kokotov·D. Korotkin
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Abstract

Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for $F^1$ in hermitian one-matrix model. We discuss the relationship between $F^1$, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian over spectral curve.

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B. Eynard, A. Kokotov, D. Korotkin. 2004-01-28. $1/N^2$ correction to free energy in hermitian two-matrix model. https://doi.org/10.1007/s11005-005-0157-9

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