Existence and uniqueness of non–Abelian vortices in a coupled quantum field theory

Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we study the non–Abelian vortices in a quantum field theory which is the two–dimensions non–Abelian vortex zeromodes coupled to the massless four–dimensions Yang–Mills modes. We establish the existence and uniqueness for vortex solutions by researching the nonlinear elliptic equations systems with exponential terms in R2 using the calculus of variations. In addition, the asymptotic behavior of the solutions at infinity and the quantized integrals in R2 are obtained.