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

A. Prats Ferrer; B. Eynard

arxiv: hep-th/0502041 · v1 · submitted 2005-02-03 · ✦ hep-th · math-ph· math.MP

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

B. Eynard , A. Prats Ferrer This is my paper

classification ✦ hep-th math-phmath.MP

keywords integralsformulamatrixmodelgrouptriangularunitaryalternative

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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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