Loop equations and topological recursion for the arbitrary-β two-matrix model

Author:

Bergère M.,Eynard B.,Marchal O.,Prats-Ferrer A.

Abstract

Abstract We write the loop equations for the β two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a “quantum” spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

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