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

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

2005-02-03

arxiv.org/abs/hep-th/0502041v1

Commun.Math.Phys. 264 (2006) 115-144

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, Latex

Scientific paper

10.1007/s00220-006-1541-8

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.

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