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Journal Articles Journal of High Energy Physics Year : 2012

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

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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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Dates and versions

cea-01117922 , version 1 (24-07-2015)

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Michel Bergère, Bertrand Eynard, O Marchal, A Prats-Ferrer. Loop equations and topological recursion for the arbitrary-β two-matrix model. Journal of High Energy Physics, 2012, pp.45. ⟨cea-01117922⟩
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