2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
High Energy Physics - Theory
2009-11-11 v1 Mathematical Physics
math.MP
Abstract
We prove that the 2-hermitean matrix model and the complex-matrix model obey the same loop equations, and as a byproduct, we find a formula for Itzykzon-Zuber's type integrals over the unitary group. Integrals over U(n) are rewritten as gaussian integrals over triangular matrices and then computed explicitly. That formula is an efficient alternative to the former Shatashvili's formula.
Cite
@article{arxiv.hep-th/0502041,
title = {2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals},
author = {B. Eynard and A. Prats Ferrer},
journal= {arXiv preprint arXiv:hep-th/0502041},
year = {2009}
}
Comments
29 pages, Latex