Bosonization in the Noncommutative Plane

TL;DR

This paper investigates the bosonization of the noncommutative massive Thirring model in 2+1 dimensions and finds that, unlike in commutative spacetime, their noncommutative versions are not equivalent at low energies.

Contribution

It demonstrates the breakdown of duality between the noncommutative massive Thirring model and Maxwell-Chern-Simons model in the low energy limit.

Findings

Noncommutative Thirring model and Maxwell-Chern-Simons model are not dual at low energies.

Duality in ordinary spacetime does not hold in the noncommutative setting.

Bosonization in noncommutative space reveals new distinctions from the commutative case.

Abstract

In this Note, we study bosonization of the noncommutative massive Thirring model in 2+1- dimensions. We show that, contrary to the duality between massive Thirring model and Maxwell-Chern-Simons model in ordinary spacetime, in the low energy (or large fermion mass) limit, their noncommutative versions are not equivalent, in the same approximation.