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

TL;DR

This paper develops a stochastic field theory model for a Dirac particle in gauge field disorder, linking concepts from QCD and condensed matter physics, and deriving effective supersymmetric sigma-models with spontaneous supersymmetry breaking.

Contribution

It introduces a novel model combining Efetov's disordered systems approach with QCD principles, replacing gauge fields with stochastic noise and deriving supersymmetric sigma-models.

Findings

Spontaneous breaking of supersymmetry in the model

Derivation of the QCD equivalent of Thouless energy

Connections established with Nambu-Jona-Lasinio and chiral perturbation theories

Abstract

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.