Second-order formalism for 3D spin-3 gravity
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Publication:4920141
DOI10.1088/0264-9381/30/3/035003zbMATH Open1266.83138arXiv1209.0894OpenAlexW3099370333MaRDI QIDQ4920141
Author name not available (Why is that?)
Publication date: 16 May 2013
Published in: (Search for Journal in Brave)
Abstract: A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection omega^a_{mu}, and substituting the result into the action integral. In the first-order formalism of the spin-3 gravity defined in terms of SL(3,R) X SL(3,R) Chern-Simons (CS) theory, however, the generalized torsion-free condition cannot be easily solved for the spin connection, because the vielbein e^a_{mu} itself is not invertible. To circumvent this problem, extra vielbein-like fields e^a_{mu
u} are introduced as a functional of e^a_{mu}. New set of affine-like connections Gamma_{mu M}^N are defined in terms of the metric-like fields, and a generalization of the Riemann curvature tensor is also presented. In terms of this generalized Riemann tensor the action integral in the second-order formalism is expressed. The transformation rules of the metric and the spin-3 gauge field under the generalized diffeomorphims are obtained explicitly. As in Einstein gravity, the new affine-like connections are related to the spin connection by a certain gauge transformation, and a gravitational CS term expressed in terms of the new connections is also presented.
Full work available at URL: https://arxiv.org/abs/1209.0894
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