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 R-2 using the calculus of variations. In addition, the asymptotic behavior of the solutions at infinity and the quantized integrals in R-2 are obtained.