Existence Theorems for Vortices in the Aharony--Bergman--Jaferis--Maldacena Model

TL;DR

This paper proves existence and uniqueness theorems for multiple vortex solutions in a supersymmetric Chern--Simons--Higgs model with bifundamental matter, extending understanding of vortex configurations in this theoretical framework.

Contribution

It establishes sharp existence and uniqueness theorems for vortices in the Aharony--Bergman--Jaferis--Maldacena model, a significant step in understanding these solutions in supersymmetric gauge theories.

Findings

Proved existence of multiple vortex solutions.

Established uniqueness of solutions under certain conditions.

Applied to the mass-deformed BPS equations in the model.

Abstract

A series of sharp existence and uniqueness theorems are established for the multiple vortex solutions in the supersymmetric Chern--Simons--Higgs theory formalism of Aharony, Bergman, Jaferis, and Maldacena, for which the Higgs bosons and Dirac fermions lie in the bifundamental representation of the general gauge symmetry group $U(N)\times U(N)$. The governing equations are of the BPS type and derived by Kim, Kim, Kwon, and Nakajima in the mass-deformed framework labeled by a continuous parameter.