Non-linear σ-model for gauge field disorder

Various studies indicate similarities between the statistical features of quantum chromodynamics (QCD) and disordered systems in condensed matter physics. To further investigate this, we propose and analytically discuss a statistical model which merges Efetovʹs approach to disordered systems with the principles of chiral symmetry and QCD. The object of our interest are the spectral fluctuations of a Dirac particle which propagates in a finite four-dimensional box under the influence of gauge fields. In our model, the gauge fields are replaced with a stochastic white noise potential, which we refer to as gauge field disorder. We arrive at effective supersymmetric non-linear σ-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 discuss various connections to other low-energy effective theories, in particular to the Nambu–Jona-Lasinio model and to chiral perturbation theory.