Topological Defects in 3-d Euclidean Gravity

TL;DR

This paper investigates topological defects in 3D Euclidean gravity, revealing their structure as monopole-vortex combinations and exploring their algebraic properties within Chern-Simons theory.

Contribution

It introduces a detailed analysis of topological defects using SO(3) spin connection decomposition and links these defects to algebraic structures in Chern-Simons theory.

Findings

Disclinations are composed of monopole and vortex structures.

The Kac-Moody algebra generated by defects is characterized.

Topological defect structures are clarified in 3D Euclidean gravity.

Abstract

By making use of the complete decomposition of SO(3) spin connection, the topological defect in 3-dimensional Euclidean gravity is studied in detail. The topological structure of disclination is given as the combination of a monopole structure and a vortex structure. Furthermore, the Kac-Moody algebra generated by the monopole and vortex is discussed in three dimensional Chern-Simons theory.