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 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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Barbero G., J.F., Basquens, M., Díaz, B. et al. Consistent and non-consistent deformations of gravitational theories. J. High Energ. Phys. 2022, 175 (2022). https://doi.org/10.1007/JHEP05(2022)175
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DOI: https://doi.org/10.1007/JHEP05(2022)175