English

Finite volume partition functions and Itzykson-Zuber integrals

High Energy Physics - Theory 2009-10-30 v2 Condensed Matter

Abstract

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.

Keywords

Cite

@article{arxiv.hep-th/9605183,
  title  = {Finite volume partition functions and Itzykson-Zuber integrals},
  author = {A. D. Jackson and M. K. Şener and J. J. M. Verbaarschot},
  journal= {arXiv preprint arXiv:hep-th/9605183},
  year   = {2009}
}

Comments

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

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