Bosonization and Duality in Arbitrary Dimensions: New Results

TL;DR

This paper explores bosonization and duality in various dimensions, establishing a general framework connecting fermionic and bosonic models, and introduces a novel higher-dimensional bosonization approach with practical applications.

Contribution

It generalizes bosonization and duality concepts to arbitrary dimensions using the doublet approach, providing new formulations and fermionic representations in four dimensions.

Findings

Established a correspondence between massive Thirring models and topologically massive gauge actions in 3D.

Generalized the bosonization structure to higher dimensions using the doublet approach.

Constructed fermionic representations for bosonic models in four dimensions.

Abstract

A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression for this relationship. We also generalize this structure to $d$ dimensions, by adopting the so-called doublet approach, recently introduced. In particular, a non- conventional formulation of the bosonization technique in higher dimensions (in the spirit of $d=3$), is proposed and, as an application, we show how fermionic (Thirring-like) representations for bosonic topologically massive models in four dimensions may be built up.