Bosonisation and Duality Symmetry in the Soldering Formalism

TL;DR

This paper introduces a soldering technique to combine dual symmetry aspects of theories, leading to new effective models and duality-invariant actions, with applications in bosonisation and electromagnetic duality.

Contribution

It develops a systematic soldering method to unify dual symmetries, producing duality-invariant master actions and exploring duality swapping in field theories.

Findings

Combines two 3D massive Thirring models into a Maxwell theory via bosonisation and soldering.

Derives duality symmetric actions and a master action with extended symmetry.

Analyzes electromagnetic duality and introduces the concept of duality swapping.

Abstract

We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional bosonisation are discussed. In particular, it is shown that 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. Similar features also hold for quantum electrodynamics in three dimensions. We also provide a systematic derivation of duality symmetric actions and show that the soldering mechanism leads to a master action which is duality invariant under a bigger set of symmetries than is usually envisaged. The concept of duality swapping is introduced and its implications are analysed. The example of electromagnetic duality is discussed in details.