On minimal mass vortex ansatz solutions to N = 2 supersymmetric Chern–Simons–Schrödinger equations

Abstract

In this short letter, we simply report the vectorial property of minimal mass solutions to N = 2 supersymmetric Chern–Simons–Schrödinger equations satisfying a standard vortex ansatz. Main purpose of the paper is to obtain an exact criterion for a minimal mass solution being vectorial, depending on parameters the equations contain. The methods employed use mass comparing arguments which are relatively simpler than counting Morse indices. Furthermore we find some vectorial solutions coming from the original Jackiw–Pi model and prove they actually coincide with the minimal mass solution at least for some range of parameters.