Description of Disclinations and Dislocations by the Chern–Simons Action for $$\mathbb{S}\mathbb{O}(3)$$ Connection

Abstract

We obtained the exact solution of the Euler–Lagrange equations following from the Chern–Simons action for $$\mathbb{S}\mathbb{O}(3)$$ connection with δ-type source. This solution is proved to describe straight linear disclination in the framework of geometric theory of defects. Torsion tensor components are calculated assuming the metric to be Euclidean. It shows that disclination can be followed by continuous distribution of dislocations with cylindrical symmetry.