# Chern--Simons term in the geometric theory of defects

## TL;DR

This paper introduces a novel application of the Chern--Simons term in the geometric theory of defects, explicitly solving for a disclination that affects the connection but not the metric, expanding understanding of geometrical defects.

## Contribution

It provides the first explicit solution describing a disclination as a defect in the connection within the geometric theory of defects.

## Key findings

- Explicit solution for a disclination in the connection
- Disclination described without metric distortion
- Computed angular rotation field for the defect

## Abstract

The Chern--Simons term is used in the geometric theory of defects. The equilibrium equations with $\delta$-function source are explicitly solved with respect to the $SO(3)$ connection. This solution describes one straight linear disclination and corresponds to the new kind of geometrical defect: it is the defect in the connection but not the metric which is the flat Euclidean metric. This is the first example of a disclination described within the geometric theory of defects. The corresponding angular rotation field is computed.