Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function

A.B. Balantekin (Wisconsin U.; Heidelberg); Madison; Max-Planck-Institute

arxiv: hep-th/0007161 · v3 · submitted 2000-07-20 · ✦ hep-th · cond-mat· hep-lat· hep-ph· nucl-th

Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function

A.B. Balantekin (Wisconsin U. , Madison , Max-Planck-Institute , Heidelberg) This is my paper

classification ✦ hep-th cond-mathep-lathep-phnucl-th

keywords characterexpansionsfunctiongivenintegralsitzykson-zuberpartitioncalculated

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A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of QCD in the sector with a given topological charge.

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