Bosonization of the Thirring Model in 2+1 Dimensions

TL;DR

This paper develops a bosonized form of the 2+1 dimensional Thirring model with a single fermion, providing insights into its nonperturbative behavior and dualities without relying on large N expansion.

Contribution

It introduces a novel bosonization approach for the 2+1D Thirring model at finite N, bridging UV and IR regimes and predicting a nontrivial UV fixed point.

Findings

Bosonized model interpolates between UV and IR regimes.

Recovers known dualities in the IR limit.

Predicts a nontrivial UV fixed point.

Abstract

In this work we provide a bosonized version of the Thirring model in 2+1 dimensions in the case of single fermion species, where we do not have the benefit of large N expansion. In this situation there are very few analytical methods to extract nonperturbative information. Meanwhile, nontrivial behavior is expected to take place precisely in this regime. To establish the bosonization of the Thirring model, we consider a deformation of a basic fermion-boson duality relation in 2+1 dimensions. The bosonized model interpolates between the ultraviolet and infrared regimes, passing several consistency checks and recovering the usual bosonization relation of the web of dualities in the infrared limit. In addition the duality predicts the existence of a nontrivial ultraviolet fixed point in the Thirring model.