Existence theorems for non-Abelian Chern--Simons--Higgs vortices with flavor
Existence theorems for non-Abelian Chern--Simons--Higgs vortices with flavor
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DOI：
10.1016/j.jde.2015.03.037
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
Shouxin Chen;Xiaosen Han;G. Lozano;F. A.Schaposnik
中科院分区：
文献类型：
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作者：
Shouxin Chen;Xiaosen Han;G. Lozano;F. A.Schaposnik
本文建立了具有规范群SU(N)×U(1)和风味SU(N)的Chern-Simons-Higgs模型的涡旋解的存在性。这些对称性通过色调锁定确保了真正的非阿贝尔涡的存在。在适当的条件下，我们将问题归结为一个具有指数项的2×2非线性椭圆型方程组。我们分别在全平面和双周期域上研究了该系统。对于平面情形，我们利用变分方法建立了解的存在性结果，并得到了解的衰减估计。在双周期域上，我们利用约束极小化方法和山路定理证明了系统至少允许两个具有相同物理能量的不同规范解。在这两种情况下，我们都得到了量子化的涡旋磁通量和电荷。
In this paper we establish the existence of vortex solutions for a Chern–Simons–Higgs model with gauge group SU (N)× 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× 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.