Consistent and non-consistent deformations of gravitational theories
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-Kucha\v{r} 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.
Cite
@article{arxiv.2202.07997,
title = {Consistent and non-consistent deformations of gravitational theories},
author = {J. Fernando Barbero G. and Marc Basquens and Bogar Díaz and Eduardo J. S. Villaseñor},
journal= {arXiv preprint arXiv:2202.07997},
year = {2022}
}
Comments
28 pages