Bosonization and Duality of Massive Thirring Model

TL;DR

This paper develops a gauge-theoretic bosonization approach for the massive Thirring model in multiple dimensions, revealing its equivalence to Maxwell-Chern-Simons and scalar field theories, with implications for non-Abelian extensions.

Contribution

It introduces a novel interpolating Lagrangian with two gauge fields for bosonizing the massive Thirring model across dimensions, emphasizing gauge invariance and extending to non-Abelian cases.

Findings

(2+1)D Thirring model maps to Maxwell-Chern-Simons theory.

(1+1)D Thirring model is equivalent to a massive free scalar.

Gauge-invariant formulation is crucial for bosonization.

Abstract

Starting from a reformulation of the Thirring model as a gauge theory, we consider the bosonization of the $D$-dimensional multiflavor massive Thirring model $(D \ge 2)$ with four-fermion interaction of the current-current type. Our method leads to a novel interpolating Lagrangian written in terms of two gauge fields. Especially we pay attention to the case of very massive fermion $m \gg 1$ in (2+1) and (1+1) dimensions. Up to the next-to-leading order of $1/m$, we show that the (2+1)-dimensional massive Thirring model is mapped to the Maxwell-Chern-Simons theory and that the (1+1)-dimensional massive Thirring model is equivalent to the massive free scalar field theory. In the process of the bosonization of the Thirring model, we point out the importance of the gauge-invariant formulation. Finally we discuss a possibility of extending this method to the non-Abelian case.