Mixed correlation functions in the 2-matrix model, and the Bethe ansatz

Using loop equation technics, we compute all mixed traces correlation functions of the 2-matrix model to large N leading order. The solution turns out to be a sort of Bethe Ansatz, i.e. all correlation functions can be decomposed on products of 2-point functions. We also find that, when the correlation functions are written collectively as a matrix, the loop equations are equivalent to commutation relations.