Finite volume partition functions and Itzykson-Zuber integrals

Details Finite volume partition functions and Itzykson-Zuber integrals Finite volume partition functions and Itzykson-Zuber integrals

1996-05-26

arxiv.org/abs/hep-th/9605183v2

Phys.Lett. B387 (1996) 355-360

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LATEX. A minor typo in equation (12) has been corrected in the revised version

Scientific paper

10.1016/0370-2693(96)00993-8

We find the finite volume QCD partition function for arbitrary quark masses. This is a generalization of a result obtained by Leutwyler and Smilga for equal quark masses. Our result is derived in the sector of zero topological charge using a generalization of the Itzykson-Zuber integral appropriate for arbitrary complex matrices. We present a conjecture regarding the result for arbitrary topological charge which reproduces the Leutwyler-Smilga result in the limit of equal quark masses. We derive a formula of the Itzykson-Zuber type for arbitrary {\em rectangular} complex matrices, extending the result of Guhr and Wettig obtained for {\em square} matrices.

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