https://doi.org/10.1140/epjc/s10052-021-09719-z
Regular Article - Theoretical Physics
Gravity in 
dimensions and realizations of the diffeomorphisms group
1
Okinawa Institute of Science and Technology Graduate University, 1919-1, Tancha, Onna, Kunigami District, 904-0495, Okinawa, Japan
2
Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743, Jena, Germany
3
SISSA, Via Bonomea, 265, 34136, Trieste, Italy
4
Università di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
5
INFN-Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
Received:
8
May
2021
Accepted:
5
October
2021
Published online:
19
October
2021
We discuss two separate realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. We renormalize them in 
dimensions, developing a new procedure for dimensional continuation of metric theories and highlighting connections with the constructions that previously appeared in the literature. Our hope is to frame candidates for ultraviolet completions of quantum gravity in 
and give some perturbative mean to assess their existence in 
, but also to speculate on some potential obstructions in the continuation of such candidates to finite values of 
. Our results suggest the presence of a conformal window in d which seems to extend to values higher than four.
© The Author(s) 2021
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