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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:

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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• http://mi.mathnet.ru/eng/tm3873
• https://doi.org/10.1134/S0371968518020103
• http://mi.mathnet.ru/eng/tm/v301/p124

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This publication is cited in the following articles:
1. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
2. V. V. Zharinov, “Hamiltonian operators with zero-divergence constraints”, Theoret. and Math. Phys., 200:1 (2019), 923–937
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