Existence of Non-Abelian Vortices in the Aharony--Bergman--Jafferis--Maldacena Theory

Details Existence of Non-Abelian Vortices in the Aharony--Bergman--Jafferis--Maldacena Theory Existence of Non-Abelian Vortices in the Aharony--Bergman--Jafferis--Maldacena Theory

2012-01-08

arxiv.org/abs/1201.1602v1

Physics

Mathematical Physics

arXiv admin note: substantial text overlap with arXiv:1106.1626 by other authors

Scientific paper

Vortices in non-Abelian gauge field theory play important roles in confinement mechanism and are governed by systems of nonlinear elliptic equations of complicated structures. In this paper, we present a series of existence and uniqueness theorems for multiple vortex solutions of the non-Abelian BPS vortex equations over R^2 and on a doubly periodic domain. Our methods are based on calculus of variations and a fixed-point argument. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are explicitly expressed in terms of several physical parameters involved.

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