Topological and Universal Aspects of Bosonized Interacting Fermionic Systems in (2+1)d

TL;DR

This paper develops a general framework for bosonizing fermionic systems in (2+1)d, revealing universal topological features and providing a clear form of the bosonized action that includes free and interacting parts.

Contribution

It establishes the universal character of the bosonized topological current and derives the explicit form of the bosonized action for interacting fermionic systems in (2+1)d.

Findings

Bosonized topological current is universal in (2+1)d.

Bosonized action comprises a Chern-Simons term and an interaction term.

Interaction effects are incorporated by replacing fermionic currents with bosonic expressions.

Abstract

General results on the structure of the bosonization of fermionic systems in $(2+1)$d are obtained. In particular, the universal character of the bosonized topological current is established and applied to generic fermionic current interactions. The final form of the bosonized action is shown to be given by the sum of two terms. The first one corresponds to the bosonization of the free fermionic action and turns out to be cast in the form of a pure Chern-Simons term, up to a suitable nonlinear field redefinition. We show that the second term, following from the bosonization of the interactions, can be obtained by simply replacing the fermionic current by the corresponding bosonized expression.