Field Theory of the Random Flux Model

TL;DR

This paper develops a supersymmetric field theory framework to analyze the long-range properties of the random flux model, revealing connections to lattice QCD and non-Hermitian operators.

Contribution

It introduces a non-linear sigma model description of the random flux model with GL(n|n) symmetry, extending to non-abelian cases and linking to quantum chromodynamics and stochastic operators.

Findings

Describes the long-range behavior using a supersymmetric non-linear sigma model.

Establishes connections between the random flux model and lattice QCD.

Identifies links to Dirac fermions in random gauge fields and non-Hermitian operators.

Abstract

The long-range properties of the random flux model (lattice fermions hopping under the influence of maximally random link disorder) are shown to be described by a supersymmetric field theory of non-linear sigma model type, where the group GL(n|n) is the global invariant manifold. An extension to non-abelian generalizations of this model identifies connections to lattice QCD, Dirac fermions in a random gauge potential, and stochastic non-Hermitian operators.