Non-linear sigma-model for gauge field disorder

Various studies indicate similarities between the statistical features of q uantum chromodynamics (QCD) and disordered systems in condensed matter phys ics. To further investigate this, we propose and analytically discuss a sta tistical model which merges Efetov's approach to disordered systems with th e principles of chiral symmetry and QCD. The object of our interest are the spectral fluctuations of a Dirac particle which propagates in a finite fou r-dimensional box under the influence of gauge fields. In our model, the ga uge fields are replaced with a stochastic white noise potential, which we r efer to as gauge field disorder. We arrive at effective supersymmetric non- linear sigma -models and spontaneous breaking of supersymmetry is found. A fundamental scale of the stochastic feature in QCD is set by the equivalent of the Thouless energy in QCD which appears naturally in our model. We dis cuss various connections to other low-energy effective theories, in particu lar to the Nambu-Jona-Lasinio model and to chiral perturbation theory. (C) 2001 Elsevier Science B.V. All rights reserved.