Chern–Simons vortices in the Gudnason model
Chern–Simons vortices in the Gudnason model
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DOI：
10.1016/j.jfa.2014.05.009
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发表时间：
2013-07
影响因子：
1.7
通讯作者：
Xiaosen Han;Changshou Lin;G. Tarantello;Yisong Yang
中科院分区：
文献类型：
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作者：
Xiaosen Han;Changshou Lin;G. Tarantello;Yisong Yang
在N= 2超对称场论的Gudnason模型中，非阿贝良规范场在对偶水平上由纯Chern-Simons动力学控制，并被实现为二维域上具有指数非线性的椭圆方程系统的解，给出了该模型中多个涡解的一系列存在性定理。在全平面情况下，我们的方法采用最小化方法，在双周期情况下，我们采用不等式约束最小化方法。对于后一种情况，我们也得到了证明任何规定的涡旋分布至少存在两个非规范解的充分条件。换句话说，有不同的解决方案具有相同的涡旋分布、能量、电和磁荷。
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.