Chern-simons vortices in the gudnason model

Xiaosen Han, Chang Shou Lin, Gabriella Tarantello, Yisong Yang

Research output: Contribution to journalArticlepeer-review


We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the N=2 supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern-Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an inequality-constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.

Original languageEnglish (US)
Pages (from-to)678-726
Number of pages49
JournalJournal of Functional Analysis
Issue number3
StatePublished - Aug 1 2014


  • Calculus of variations
  • Systems of nonlinear elliptic equations
  • Vortices in gauge field theory

ASJC Scopus subject areas

  • Analysis


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