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

Michel Bergère (1) , Bertrand Eynard (1, 2) , O Marchal (3) , A Prats-Ferrer (4)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 CERN [Genève]
3 University of Alberta
4 Concordia University [Montreal]

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.

Domains: Physics [physics]

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⟩