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Dynamical symmetries in topological 3D gravity with torsion

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Il Nuovo Cimento B (1971-1996)

Summary

Recently two of us generalized the topological massive gauge model of gravity of Deser, Jackiw, and Templeton (DJT) by liberating its translational gauge degrees of freedom. Consequently, the newR 3◯SO(1,2) gauge model «lives» in a 3-dimensional Riemann-Cartan space-time with torsion. The extended Lagrangian consists, of the familiar Einstein-Cartan term, the Chern-Simons 3-form for the curvature, and, in addition, of a new translational Chern-Simons term. In this article we uncover a «dynamical symmetry» of the new theory by inquiring how the two Noether identities, the two Bianchi identities, and the two field equations are interrelated to each other. This includes two important subcases in which the first Bianchi identity is mapped into the second one and the first (energy-momentum) Noether into the second (angular-momentum) Noether identity. As a furtherexact result, the topological gauge field equations imply a covariant Proca-type field equation, for the translational gauge potential,i.e. the coframe. Thus the theory encompasses massive gravitons, as in the DJT model.

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Author notes

  1. E. W. Mielke & F. W. Hehl

    Present address: Institute for Theoretical Physics, University of Cologne, D(W)-5000, Köln 41, Germany

  2. P. Baekler

    Present address: Vereinigte Aluminium-Werke AG, Postfach 2448, D-5300, Bonn 1

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, D(W)-5000, Köln 41, Germany

    P. Baekler

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  1. P. Baekler
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  2. E. W. Mielke
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  3. F. W. Hehl
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Additional information

Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.

Supported by the Deutsche Forschungsgemeinschaft, Bonn, project He 528/12-1, and by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.

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Baekler, P., Mielke, E.W. & Hehl, F.W. Dynamical symmetries in topological 3D gravity with torsion. Nuov Cim B 107, 91–110 (1992). https://doi.org/10.1007/BF02726888

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  • DOI: https://doi.org/10.1007/BF02726888

PACS 04.50

PACS 04.60

PACS 12.25

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