Abstract
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 \({\mathbb{R}^2}\) 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
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.
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Communicated by Marcos Marino.
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Chen, S., Zhang, R. & Zhu, M. Multiple Vortices in the Aharony–Bergman–Jafferis–Maldacena Model. Ann. Henri Poincaré 14, 1169–1192 (2013). https://doi.org/10.1007/s00023-012-0209-5
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DOI: https://doi.org/10.1007/s00023-012-0209-5