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We discuss two distinct realizations of the diffeomorphism group for metricgravity, which give rise to theories that are classically equivalent, butquantum mechanically distinct. We renormalize them in $d=2+\epsilon$dimensions, developing a new procedure for dimensional continuation of metrictheories and highlighting connections with the constructions that previouslyappeared in the literature. Our hope is to frame candidates ultravioletcompletions of quantum gravity in $d>2$ and give some perturbative mean toassess its existence in $d=4$, but also to speculate on some potentialobstructions in the continuation of such candidates to finite values of$\epsilon$. Our results suggest the presence of a conformal window in $d$ whichseems to extend to values higher than four.

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