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

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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  • HAL Id : cea-01117922, version 1
  • ARXIV : 1106.0332

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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, Springer, 2012, pp.45. ⟨cea-01117922⟩

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