Soldering Formalism in Noncommutative Field Theory: A Brief Note

TL;DR

This paper extends the soldering formalism to noncommutative planar field theories, demonstrating how two noncommutative Maxwell-Chern-Simons theories can be fused into a noncommutative Proca model with quadratic corrections.

Contribution

It introduces the soldering formalism into noncommutative field theories and shows how to combine two opposite-sign Maxwell-Chern-Simons theories into a noncommutative Proca model.

Findings

Soldering of noncommutative Maxwell-Chern-Simons theories yields a noncommutative Proca model.

The resulting model includes quadratic corrections in the noncommutativity parameter.

The work highlights the role of gauge invariance in the soldering process.

Abstract

In this paper, I develop the Soldering formalism in a new domain - the noncommutative planar field theories. The Soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well-known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present work is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance, (or the lack of it), in the above soldering process, is revealed in an interesting way.