Sharp existence and uniqueness theorems for non-Abelian multiple vortex solutions |
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Authors: | Chang-Shou Lin Yisong Yang |
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Affiliation: | 1. Department of Mathematics, National Taiwan University, Taipei, Taiwan 10617, ROC;2. Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, NY 11201, USA |
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Abstract: | Vortices in non-Abelian gauge field theory play essential roles in the mechanism of color confinement and are governed by systems of nonlinear elliptic equations of complicated structure. In this paper, we present a series of sharp existence and uniqueness theorems for multiple vortex solutions of the non-Abelian BPS equations over R2 and on a doubly periodic domain. Our methods are based on calculus of variations which may be used to analyze more extended problems. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are expressed in terms of physical parameters involved explicitly. |
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Keywords: | Non-Abelian gauge field theory BPS vortices Confinement Higgs condensed solitons Existence and uniqueness |
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