First Order Formalism for Generalized Vortices

TL;DR

This paper develops a formalism to construct generalized vortex models that support stressless solutions obeying first order equations, enabling energy calculation without explicit solutions.

Contribution

It introduces a systematic procedure to derive Lagrangian densities for generalized vortex models with stressless conditions and first order equations.

Findings

Derived constraints on Lagrangian densities for vortex models.

Introduced an auxiliary function for energy computation.

Supported models generalizing Maxwell-Higgs and Chern-Simons-Higgs vortices.

Abstract

This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the construction of models that support vortices that obey the stressless condition and lead to first order differential equations which are compatible with the equations of motion. The results induce the appearance of constraints that restrict the choice of the Lagrangian densities, but help us to introduce an auxiliary function that allows to calculate the energy without knowing the explicit form of the solutions.