Aharony-Bergman-Jafferis-Maldacena理论中非Abel涡旋的存在性
Existence of Non-Abelian Vortices in the Aharony--Bergman--Jafferis--Maldacena Theory
摘要：
非阿贝尔规范场理论中的涡旋在禁闭机制中起着重要的作用，它由复杂结构的非线性椭圆方程组所控制。本文给出了R^2上双周期区域上非Abel BPS涡方程多涡解的存在唯一性定理。我们的方法是基于变分法和一个不动点参数。在双周期情况下，存在唯一解的充分必要条件被明确地表示为几个物理参数。
英文摘要：
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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