## Loop equations and topological recursion for the arbitrary-$β$ two-matrix model    [PDF]

Michel Bergère, Bertrand Eynard, Olivier Marchal, Aleix Prats-Ferrer
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.
View original: http://arxiv.org/abs/1106.0332