Magnetic Fields and Fractional Statistics in Boundary Conformal Field Theory

TL;DR

This paper explores boundary conformal field theories with magnetic interactions that induce fractional statistics, analyzing their phase structure through exact and approximate Coulomb gas models relevant to string theory and quantum Hall systems.

Contribution

It introduces new exact and approximate results for a generalized Coulomb gas with magnetic-induced fractional statistics in boundary conformal field theories.

Findings

Magnetic interactions induce fractional statistics in boundary CFTs.

The phase structure of the Coulomb gas is significantly affected by these fractional statistics.

New analytical results enhance understanding of such models in string theory and quantum Hall contexts.

Abstract

We study conformal field theories describing two massless one-dimensional fields interacting at a single spatial point. The interactions we include are periodic functions of the bosonized fields separately plus a ``magnetic'' interaction that mixes the two fields. Such models arise in open string theory and dissipative quantum mechanics and perhaps in edge state tunneling in the fractional quantized Hall effect. The partition function for such theories is a Coulomb gas with interchange phases arising from the magnetic field. These ``fractional statistics'' have a profound effect on the phase structure of the Coulomb gas. In this paper we present new exact and approximate results for this type of generalized Coulomb gas.