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.
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Bergère, M., Eynard, B., Marchal, O. et al. Loop equations and topological recursion for the arbitrary-β two-matrix model. J. High Energ. Phys. 2012, 98 (2012). https://doi.org/10.1007/JHEP03(2012)098
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DOI: https://doi.org/10.1007/JHEP03(2012)098