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 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 and give some perturbative mean to assess their existence in d= 4 , but also to speculate on some potential obstructions in the continuation of such candidates to finite values of ϵ. Our results suggest the presence of a conformal window in d which seems to extend to values higher than four.

Gravity in d=2+ϵ dimensions and realizations of the diffeomorphisms group

Del Porro F.;Zanusso O.
2021-01-01

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 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 and give some perturbative mean to assess their existence in d= 4 , but also to speculate on some potential obstructions in the continuation of such candidates to finite values of ϵ. Our results suggest the presence of a conformal window in d which seems to extend to values higher than four.
2021
Martini, R.; Ugolotti, A.; Del Porro, F.; Zanusso, O.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1121001
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