Exponentially generalized vortex

TL;DR

This paper introduces an exponentially generalized Abelian model to study vortex structures coupled with Maxwell and Chern-Simons fields, analyzing their static configurations and energy degeneracies.

Contribution

It presents a novel exponentially generalized Abelian model and explores vortex solutions, revealing different energy degeneracy factors in Maxwell and Chern-Simons cases.

Findings

Scalar field solutions produce degenerate minima with factor ν² in Maxwell case.

In Chern-Simons case, solutions are degenerate by factor κν²/a_s.

Numerical solutions of Bogomol'nyi equations are discussed.

Abstract

In this work, we propose an exponentially generalized Abelian model. We investigated the presence of vortex structures in models coupled to Maxwell and Chern-Simons fields. We chose to investigate the dynamics of the complex scalar field in models coupled separately to the Maxwell term and the Chern-Simons term. For this, we analyze the Bogomol'nyi equations in both cases to describe the static field configurations. An interesting result appears when we note that scalar field solutions generate degenerate minimum energy configurations by a factor of $\nu^{2}$ in Maxwell's case. On the other hand, in the case of Chern-Simons, the solutions in this sector are degenerate by a factor of $\kappa\nu^{2}/a_{s}$. Finally, we solve the Bogomol'nyi equations numerically and discuss our results.