Existence of solutions to relativistic non-Abelian Chern-Simons-Higgs vortex equations on graphs

TL;DR

This paper proves the existence of solutions to relativistic non-Abelian Chern-Simons-Higgs vortex equations defined on finite graphs, expanding the understanding of such equations in discrete settings.

Contribution

It establishes the first existence results for these vortex equations on finite graphs, bridging continuous and discrete mathematical physics models.

Findings

Existence of solutions on finite graphs proven.

Method applicable to other discrete gauge theories.

Advances understanding of vortex equations in graph-based models.

Abstract

Let $G=(V,E)$ be a connected finite graph. We study the relativistic non-Abelian Chern-Simons-Higgs vortex equations on the graph $G$. We establish an existence result to the relativistic non-Abelian Chern-Simons-Higgs vortex equations.