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Is There Any Symmetry Left in Gravity Theories with Explicit Lorentz Violation?

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Ciudad de México 04510, Mexico
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Symmetry 2018, 10(10), 433; https://doi.org/10.3390/sym10100433
Received: 15 August 2018 / Revised: 14 September 2018 / Accepted: 18 September 2018 / Published: 25 September 2018
(This article belongs to the Special Issue Broken Symmetry in Curved Spacetime and Gravity)
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Abstract

It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the first-order formalism and that can be regarded as a set of improved diffeomorphisms. These symmetries are known as local translations, and among other features, they are Lorentz covariant off shell. It is thus interesting to study if theories with explicit Lorentz violation are invariant under local translations. In this work, an example of such a theory, known as the minimal gravity sector of the Standard Model Extension, is analyzed. Using a robust algorithm, it is shown that local translations are not a symmetry of the theory. It remains to be seen if local translations are spontaneously broken under spontaneous Lorentz violation, which are regarded as a more natural alternative when spacetime is dynamic. View Full-Text
Keywords: local Lorentz invariance; diffeomorphism invariance; local translations; first-order formalism local Lorentz invariance; diffeomorphism invariance; local translations; first-order formalism
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bonder, Y.; Corral, C. Is There Any Symmetry Left in Gravity Theories with Explicit Lorentz Violation? Symmetry 2018, 10, 433.

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