Bosonisation and Soldering of Dual Symmetries in Two and Three Dimensions

TL;DR

This paper introduces a novel soldering technique that combines dual symmetries from bosonised fermionic models in two and three dimensions, leading to new effective theories and insights into their correlation functions.

Contribution

The paper develops a new soldering method to unify dual symmetries in bosonised models, producing results not accessible by previous approaches.

Findings

Reproduces the Schwinger and Thirring models through soldering in 2D.

Combines 3D Thirring models to derive an effective Maxwell theory.

Provides consistent correlation functions for the effective theories.

Abstract

We develop a technique that solders the dual aspects of some symmetry following from the bosonisation of two distinct fermionic models, thereby leading to new results which cannot be otherwise obtained. Exploiting this technique, the two dimensional chiral determinants with opposite chirality are soldered to reproduce either the usual gauge invariant expression leading to the Schwinger model or, alternatively, the Thirring model. Likewise, two apparently independent three dimensional massive Thirring models with same coupling but opposite mass signatures, in the long wavelegth limit, combine by the process of bosonisation and soldering to yield an effective massive Maxwell theory. The current bosonisation formulas are given, both in the original independent formulation as well as the effective theory, and shown to yield consistent results for the correlation functions. Similar features also hold for quantum electrodynamics in three dimensions.