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Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 124–143 (Mi tm3873)  

Chern–Simons action and disclinations

M. O. Katanaevab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya ul. 35, Kazan, 420008 Russia

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
The work was partly supported by the Russian Government Program of Competitive Growth of Kazan Federal University.


DOI: https://doi.org/10.1134/S0371968518020103

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 114–133

Bibliographic databases:

Document Type: Article
UDC: 517.958:539.3
Received: July 25, 2017

Citation: M. O. Katanaev, “Chern–Simons action and disclinations”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 124–143; Proc. Steklov Inst. Math., 301 (2018), 114–133

Citation in format AMSBIB
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\paper Chern--Simons action and disclinations
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\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 301
\pages 124--143
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • http://mi.mathnet.ru/eng/tm3873
  • https://doi.org/10.1134/S0371968518020103
  • http://mi.mathnet.ru/eng/tm/v301/p124

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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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