Consistent and non-consistent deformations of gravitational theories Articles uri icon

publication date

  • May 2022

start page

  • 1

end page

  • 29


  • 5, 175


  • 2022

International Standard Serial Number (ISSN)

  • 1029-8479

Electronic International Standard Serial Number (EISSN)

  • 1126-6708


  • 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-Kuchar 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.


  • Materials science and engineering
  • Mathematics
  • Physics


  • chern-simons theories; classical theories of gravity; gauge symmetry; topological field theories