Topological quantization of self-dual Chern-Simons vortices on Riemann Surfaces

TL;DR

This paper investigates the self-duality equations of Chern-Simons Higgs theory on curved Riemann surfaces, proving magnetic flux quantization and deriving vortex equations with topological terms, advancing understanding of topological quantization in curved backgrounds.

Contribution

It introduces a novel gauge potential decomposition method to rigorously prove magnetic flux quantization and derive vortex equations with topological terms in curved spacetime.

Findings

Magnetic flux is quantized in curved spacetime.

The unit magnetic flux in curved spacetime is identified.

Self-dual vortex equations with topological terms are derived.

Abstract

The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and $\phi$-mapping method. The special form of the gauge potential decomposition is obtained directly from the first of the self-duality equations. Using this decomposition, a rigorous proof of magnetic flux quantization in background curved spacetime is given and the unit magnetic flux in curved spacetime is also found . Furthermore, the precise self-dual vortex equation with topological term is obtained, in which the topological term has always been ignored.