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

• Autores: Chen, Shouxin; Han, Xiaosen; Lozano, Gustavo; Schaposnik, Fidel Arturo
• Año de publicación: 2015
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Físicas; Chern–Simons–Higgs equations; BPS equations; Topological solutions; Doubly periodic solutions; Existence theorems
• Institución: Comisión de Investigaciones Científicas de la Provincia de Buenos Aires

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 ensuring 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 ellip- tic 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 solu- tions. 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 mini- mization approach and the mountain-pass theorem. In both cases we get the quantized vortex magnetic fluxes and electric charges.