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

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 (i...

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Detalles Bibliográficos
Autores principales: Bergere, Michel, Eynard, Bertrand, Marchal, Olivier, Prats-Ferrer, Aleix
Lenguaje:eng
Publicado: 2011
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP03(2012)098
http://cds.cern.ch/record/1356017
Descripción
Sumario: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.