On the equivalence of the self-dual and Maxwell-Chern-Simons models coupled to Fermions

TL;DR

This paper demonstrates the exact quantum equivalence between the self-dual and Maxwell-Chern-Simons models coupled to fermions, highlighting the necessity of a Thirring-like interaction for equivalence.

Contribution

It establishes the quantum equivalence of the models with non-minimal coupling, including the role of a Thirring-like interaction, using functional methods.

Findings

Models are equivalent only with a Thirring-like interaction.

Equivalence persists at quantum level after renormalization.

Fermion sectors match under the specified conditions.

Abstract

We study the exact equivalence between the self-dual model minimally coupled with a Dirac field and the Maxwell-Chern-Simons model with non-minimal magnetic coupling to fermions. We show that the fermion sectors of the models are equivalent only if a Thirring like interaction is included. Using functional methods we verify that, up to renormalizations, the equivalence persists at the quantum level.