Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Chen, Shouxin¹  Han, Xiaosen^1,2  Lozano, Gustavo^3,4  Schaposnik, Fidel A.⁵ 

[1] Henan Univ, Sch Math & Stat, Inst Contemporary Math, Kaifeng 475004, Henan, Peoples R China

[2] Natl Taiwan Univ, Ctr Adv Study Theoret Sci, Taida Inst Math Sci, Taipei 10617, Taiwan

[3] Univ Buenos Aires, FCEyN, Dept Fis, RA-1428 Buenos Aires, DF, Argentina

[4] Univ Buenos Aires, FCEyN, Inst Fis Buenos Aires, RA-1428 Buenos Aires, DF, Argentina

[5] Univ Nacl La Plata, Dept Fis, Inst Fis La Plata, RA-1900 La Plata, Buenos Aires, Argentina

关键词: Chern-Simons-Higgs equations;    BPS equations;    Topological solutions;    Doubly periodic solutions;    Existence theorems;   

DOI  :  10.1016/j.jde.2015.03.037

来源: Elsevier

【 摘 要 】

In this paper we establish the existence of vortex solutions for a Chern-Simons-Higgs model with gauge group SU(N) x U(1) and flavor SU(N). These symmetries ensure the existence of genuine non-Abelian vortices through a color flavor locking. Under a suitable ansatz we reduce the problem to a 2 x 2 system of nonlinear elliptic equations with exponential terms. We study this system over the full plane and over a doubly periodic domain, respectively. For the planar case we use a variational argument to establish the existence result and derive the decay estimates of the solutions. Over the doubly periodic domain we show that the system admits at least two gauge-distinct solutions carrying the same physical energy by using a constrained minimization approach and the mountain-pass theorem. In both cases we get the quantized vortex magnetic fluxes and electric charges. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free