Existence of non-Abelian vortices in a coupled 4D-2D quantum field theory

TL;DR

This paper proves the existence and uniqueness of non-Abelian vortex solutions in a coupled 4D-2D quantum field theory, analyzing their asymptotic behavior and quantized properties using variational methods.

Contribution

It establishes the first rigorous proof of non-Abelian vortex solutions in a coupled 4D-2D setting, including their asymptotics and quantization.

Findings

Existence and uniqueness of solutions proven

Asymptotic behavior characterized

Quantized integrals computed

Abstract

Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the gauged non-Abelian vortices in a coupled 4D-2D quantum field theory by researching the nonlinear elliptic equations systems with exponential terms in $\mathbb{R}^{2}$ using the calculus of variations. In addition, we obtain the asymptotic behavior of the solutions at infinity and the quantized integrals in $\mathbb{R}^{2}$.