Chiral random matrix theory and QCD
Abstract
As was shown by Leutwyler and Smilga, the fact that chiral symmetry is broken and the existence of a effective finite volume partition function leads to an infinite number of sum rules for the eigenvalues of the Dirac operator in QCD. In this paper we argue these constraints, together with universality arguments from quantum chaos and universal conductance fluctuations, completely determine its spectrum near zero virtuality. As in the classical random matrix ensembles, we find three universality classes, depedending on whether the color representation of the gauge group is pseudoreal, complex or real. They correspond to $SU(2)$ with fundamental fermions, $SU(N_c)$, $N_c \ge 3$, with fundamental fermions, and $SU(N_c)$, $N_c \ge 3$, with adjoint fermions, respectively.}
 Publication:

arXiv eprints
 Pub Date:
 May 1994
 arXiv:
 arXiv:hepth/9405006
 Bibcode:
 1994hep.th....5006V
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter
 EPrint:
 16 pages and 4 figures (available upon request), SUNYNTG94/20