Existence Of Non-abelian Vortices In The Aharony-bergman-jafferis-maldacena Theory

Vortices in non-Abelian gauge field theory play important roles in confinement mech-anism and are governed by systems of nonlinear elliptic equations of complicated struc-tures. In this paper, we present a series of existence and uniqueness theorems for multiplevortex solutions of the non-Abelian BPS vortex equations on a doubly periodic domain.Our methods are based on calculus of variations and a fixed-point argument. The neces-sary and sufcient conditions for the existence of a unique solution in the doubly periodicsituation are explicitly expressed in terms of several physical parameters involved.