Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantu m chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a fin ite four-dimensional box in the presence of gauge fields. We construct a mo del which combines Efetov's approach to disordered systems with the princip les of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effectiv e supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thoul ess energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.