科研之友
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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 BPS vortex equations, arising in the dual-layered Chern-Simons field theory developed by Aharony, Bergman, Jafferis, and Maldacena, over R-2 and on a doubly periodic domain. In the full-plane setting, we show that the solution realizing a prescribed distribution of vortices exists and is unique. In the compact setting, we show that a solution realizing n prescribed vortices exists over a doubly periodic domain Omega if and only if the condition n < lambda vertical bar Omega vertical bar/2 pi holds, where lambda > 0 is the Higgs coupling constant. In this case, if a solution exists, it must be unique. Our methods are based on calculus of variations.
- 出版日期2013-7
- 单位河南大学
