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arXiv · 2202.07997

Consistent and non-consistent deformations of gravitational theories

J. Fernando Barbero G.·Marc Basquens·Bogar Díaz·Eduardo J. S. Villaseñor
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Abstract

We study the internally abelianized version of a range of gravitational theories, written in connection tetrad form, and study the possible interaction terms that can be added to them in a consistent way. We do this for 2+1 dimensional and 3+1 dimensional models. In the latter case we show that the Cartan-Palatini and Holst actions are not consistent deformations of their abelianized versions. We also show that the Husain-Kuchař and Euclidean self-dual actions are consistent deformations of their abelianized counterparts. This suggests that if the latter can be quantized, it could be possible to devise a perturbative scheme leading to the quantization of Euclidean general relativity along the lines put forward by Smolin in the early nineties.

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J. Fernando Barbero G., Marc Basquens, Bogar Díaz, Eduardo J. S. Villaseñor. 2022-05-27. Consistent and non-consistent deformations of gravitational theories. https://doi.org/10.1007/jhep05(2022)175

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