On The Random Vector Potential Model In Two Dimensions

TL;DR

This paper investigates the two-dimensional random vector potential model for massless fermions, providing exact solutions for the abelian case and demonstrating asymptotic freedom and algebraic correlation functions in the non-abelian case.

Contribution

It offers a complete solution to the abelian model via bosonization and introduces a novel approach to compute non-abelian correlation functions exactly without replicas or supersymmetry.

Findings

Abelian model solved exactly using bosonization.

Non-abelian model shown to be asymptotically free at large distances.

Exact algebraic form of quenched chiral current correlations obtained.

Abstract

The random vector potential model describes massless fermions coupled to a quenched random gauge field. We study its abelian and non-abelian versions. The abelian version can be completely solved using bosonization. We analyse the non-abelian model using its supersymmetric formulation and show, by a perturbative renormalisation group computation, that it is asymptotically free at large distances. We also show that all the quenched chiral current correlation functions can be computed exactly, without using the replica trick or the supersymmetric formulation, but using an exact expression for the effective action for any sample of the random gauge field. These chiral correlation functions are purely algebraic.