On some integrals over the U(N) unitary group and their large N limit

J.-B. Zuber; P. Zinn-Justin

On some integrals over the U(N) unitary group and their large N limit

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arxiv math-ph/0209019 v3 pith:MM67T3AX submitted 2002-09-10 math-ph cond-mathep-thmath.COmath.MP

P. Zinn-Justin , J.-B. Zuber This is my paper · ORCID

classification math-phcond-mathep-thmath.COmath.MP

keywords grouplargelimitunitaryapproachescombinatoricsdaggerdeals

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abstract

The integral over the U(N) unitary group $I=\int DU \exp\Tr A U B U^\dagger$ is reexamined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and on what they teach us on the large $N$ limit of $\log I$.

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