Bosonization of Thirring Model in Arbitrary Dimension

TL;DR

This paper introduces a new master Lagrangian approach for bosonizing the massive Thirring model in arbitrary dimensions, establishing equivalences with other theories and extending known results.

Contribution

The authors develop a novel master Lagrangian that unifies previous interpolating Lagrangians for bosonization across dimensions and provides alternative proofs of known equivalences.

Findings

Proves equivalence of Thirring model and Maxwell-Chern-Simons theory in (2+1)D.

Shows bosonized (3+1)D Thirring model is equivalent to antisymmetric tensor gauge theory.

Reproduces known bosonization results in (1+1)D.

Abstract

We propose to use a novel master Lagrangian for performing the bosonization of the $D$-dimensional massive Thirring model in $D=d+1 \ge 2$ dimensions. It is shown that our master Lagrangian is able to relate the previous interpolating Lagrangians each other which have been recently used to show the equivalence of the massive Thirring model in (2+1) dimensions with the Maxwell-Chern-Simons theory. Starting from the phase-space path integral representation of the master Lagrangian, we give an alternative proof for this equivalence up to the next-to-leading order in the expansion of the inverse fermion mass. Moreover, in (3+1)-dimensional case, the bosonized theory is shown to be equivalent to the massive antisymmetric tensor gauge theory. As a byproduct, we reproduce the well-known result on bosonization of the (1+1)-dimensional Thirring model following the same strategy. Finally a possibility of extending our strategy to the non-Abelian case is also discussed.