On the question of regular solitons in a Noncommutative Maxwell--Chern--Simons--Higgs model

TL;DR

This paper investigates regular soliton solutions in a noncommutative Maxwell--Chern--Simons--Higgs model, demonstrating the absence of regular non-trivial solutions satisfying certain bounds, using an alternative approach that remains well-behaved as the noncommutativity parameter approaches zero.

Contribution

It introduces an alternative method to analyze noncommutative solitons that remains regular in the commutative limit, contrasting with the singular results from the operator formalism.

Findings

No regular non-trivial solutions satisfying B--P--S bound were found.

The alternative approach is complementary to the operator formalism.

Regularity in the $ heta o 0$ limit was achieved with this method.

Abstract

The Maxwell--Chern--Simons model with scaler matter in the adjoint representation is analyzed from an alternative approach which is regular in the $\theta \to 0$ limit. This method is complementary to the usual operator formalism applied to explore the nonperturbative solutions which gives singular results in the $\theta \to 0$ limit. The absence of any regular non-trivial lumpy solutions satisfying B--P--S bound has been conclusively demonstrated.