Non-topological Vortex Configurations in the ABJM Model

Abstract

In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony--Bergman--Jafferis--Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic $2\times 2$ system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that, any positive energy level is attained by a 1-parameter family of vortex solutions which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a "quantization" effect nor an energy gap is induced upon the system by the rigid "critical" coupling of the self-dual regime.