Chern—Simons Action and Disclinations

Abstract

We review the main properties of the Chern—Simons and Hilbert—Einstein actions on a three-dimensional manifold with Riemannian metric and torsion. We show a connection between these actions that is based on the gauge model for the inhomogeneous rotation group. The exact solution of the Euler—Lagrange equations is found for the Chern—Simons action with the linear source. This solution is proved to describe one straight linear disclination in the geometric theory of defects.