Thirring model as a gauge theory

Abstract

We give another reformulation of the Thirring model (with four-fern-don 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 (respectively critical four-fermion coupling G c ) as a function of the four-fermion coupling G(respectively N), below (respectively above) which the chiral symmetry is spontaneously broken.