Sharp existence and uniqueness theorems for non-Abelian multiple vortex solutions

Chang Shou Lin, Yisong Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)650-676
Number of pages27
JournalNuclear Physics B
Issue number3
StatePublished - May 21 2011


  • BPS vortices
  • Confinement
  • Existence and uniqueness
  • Higgs condensed solitons
  • Non-Abelian gauge field theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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