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arXiv · 1106.0332

Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model

Michel Bergère·Bertrand Eynard·Olivier Marchal·Aleix Prats-Ferrer
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Abstract

We write the loop equations for the $\beta$ 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.

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Michel Bergère, Bertrand Eynard, Olivier Marchal, Aleix Prats-Ferrer. 2011-06-01. Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model. https://doi.org/10.1007/jhep03(2012)098

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