  Recent theoretical and numerical developments show analogies between quantum
chromodynamics (QCD) and disordered systems in condensed matter physics. We
study the spectral fluctuations of a Dirac particle propagating in a finite
four dimensional box in the presence of gauge fields. We construct a model
which combines Efetov's approach to disordered systems with the principles of
chiral symmetry and QCD. To this end, the gauge fields are replaced with a
stochastic white noise potential, the gauge field disorder. Effective
supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of
supersymmetry is found. We rigorously derive the equivalent of the Thouless
energy in QCD. Connections to other low-energy effective theories, in
particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are
found.
