2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals

摘要

We prove that the 2-hermitean matrix model and the complex-matrix model obeythe same loop equations, and as a byproduct, we find a formula forItzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) arerewritten as gaussian integrals over triangular matrices and then computedexplicitly. That formula is an efficient alternative to the formerShatashvili's formula.