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Article Dans Une Revue Journal of High Energy Physics Année : 2012

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

Résumé

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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Dates et versions

hal-00863705 , version 1 (19-09-2013)

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Michel Bergere, Bertrand Eynard, Olivier Marchal, Aleix Prats Ferrer. Loop equations and topological recursion for the arbitrary β two-matrix model. Journal of High Energy Physics, 2012, pp.JHEP03(2012)098. ⟨10.1007/JHEP03(2012)098⟩. ⟨hal-00863705⟩
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