Spectral sum rules and Selberg's integral

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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10 pages, SUNY-NTG-94/6

Scientific paper

10.1016/0370-2693(94)90784-6

Using Selberg's integral formula we derive all Leutwyler-Smilga type sum rules for one and two flavors, and for each of the three chiral random matrix ensembles. In agreement with arguments from effective field theory, all sum rules for $N_f = 1$ coincide for the three ensembles. The connection between spectral correlations and the low-energy effective partition function is discussed.

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