Gravity in dimensions and realizations of the diffeomorphisms group

Riccardo Martini; Alessandro Ugolotti; Francesco Del Porro; Omar Zanusso

doi:10.1140/epjc/s10052-021-09719-z

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 916
https://doi.org/10.1140/epjc/s10052-021-09719-z

Regular Article - Theoretical Physics

Gravity in $d = 2 + ϵ$ ${\varvec{d=2+\epsilon }}$ dimensions and realizations of the diffeomorphisms group

Riccardo Martini¹^a, Alessandro Ugolotti², Francesco Del Porro³ and Omar Zanusso⁴^,5

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

^a riccardo.martini@oist.jp

Received: 8 May 2021
Accepted: 5 October 2021
Published online: 19 October 2021

Abstract

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 $d = 2 + ϵ$ $d=2+\epsilon$ 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 $d > 2$ $$d>2$$ and give some perturbative mean to assess their existence in $d = 4$ $$d=4$$ , but also to speculate on some potential obstructions in the continuation of such candidates to finite values of $ϵ$ $\epsilon$ . 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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