Non-topological condensates for the self-dual Chern-Simons-Higgs model

TL;DR

This paper proves the existence of non-topological vortex condensates in the self-dual Chern-Simons-Higgs model as the Chern-Simons parameter approaches zero, addressing a longstanding physical and mathematical question.

Contribution

It establishes the existence of non-topological condensates with concentrated magnetic fields in the model as the parameter tends to zero, filling a key gap in the theory.

Findings

Existence of non-topological condensates confirmed as $k o 0$

Magnetic field concentrated at vortex points as Dirac measures

Addresses a long-standing open problem in the field

Abstract

For the abelian self-dual Chern-Simons-Higgs model we address existence issues of periodic vortex configurations -- the so-called condensates-- of non-topological type as $k \to 0$, where $k>0$ is the Chern-Simons parameter. We provide a positive answer to the long-standing problem on the existence of non-topological condensates with magnetic field concentrated at some of the vortex points (as a sum of Dirac measures) as $k \to 0$, a question which is of definite physical interest.