The U(1) Topological Gauge Field Theory for Topological Defects in Liquid Crystals

TL;DR

This paper develops a U(1) topological gauge field theory to describe topological defects in liquid crystals, revealing how monopoles and strings are characterized by topological charges and spatial dimensions.

Contribution

It introduces a novel U(1) gauge theory invariant under director inversion, using gauge potential decomposition and $\phi$-mapping to unify the description of defects.

Findings

Monopoles and strings are distinguished by their spatial dimensions.

Topological charges correspond to winding numbers of the $\phi$-mapping.

The theory provides a unified topological current for defects.

Abstract

A novel U(1) topological gauge field theory for topological defects in liquid crystals is constructed by considering the U(1) gauge field is invariant under the director inversion. Via the U(1) gauge potential decomposition theory and the $\phi$-mapping topological current theory, the decomposition expression of U(1) gauge field and the unified topological current for monopoles and strings in liquid crystals are obtained. It is revealed that monopoles and strings are located in different spatial dimensions and their topological charges are just the winding numbers of $\phi$-mapping.