Thirring Model as a Gauge Theory

TL;DR

This paper reformulates the Thirring model as a gauge theory, using the Batalin-Fradkin formalism, and analyzes chiral symmetry breaking, identifying a second order phase transition with explicit critical parameters.

Contribution

It provides a novel gauge-theoretic reformulation of the Thirring model and studies its chiral phase transition using the Batalin-Fradkin formalism and large N expansion.

Findings

Existence of a second order chiral phase transition.

Explicit critical number of flavors $N_c$ and coupling $G_c$ identified.

Chiral symmetry breaking occurs below $N_c$ or $G_c$.

Abstract

We give another reformulation of the Thirring model (with four-fermion interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of the corresponding gauge theory according to the Batalin-Fradkin formalism. Based on this formalism, we study the chiral symmetry breaking of the $D$-dimensional Thirring model ($2<D<4$) with $N$ flavors of 4-component fermions. By constructing the gauge covariant effective potential for the chiral order parameter, up to the leading order of $1/N$ expansion, we show the existence of the second order chiral phase transition and obtain explicitly the critical number of flavors $N_c$ (resp. critical four-fermion coupling $G_c$) as a function of the four-fermion coupling $G$ (resp. $N$), below (resp. above) which the chiral symmetry is spontaneously broken.