The continuum limit of quantum gravity at first order in perturbation theory

Abstract

The Wilsonian renormalization group (RG) properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity, which is however non-perturbative in. The ultraviolet part of the renormalized trajectory lies outside the diffeomorphism invariant subspace, entering this subspace only in the infrared, below a dynamically generated amplitude suppression scale. Interactions are dressed with coefficient functions of the conformal factor, their form being determined by the RG. In the ultraviolet, the coefficient functions are parametrised by an infinite number of underlying couplings. Choosing these couplings appropriately, the coefficient functions trivialise on entering the diffeomorphism invariant subspace. Here, dynamically generated effective diffeomorphism couplings emerge, including Newton's constant. In terms of the Legendre effective action, we establish the continuum limit to first order, characterising the most general form of such coefficient functions so as to verify universality.

Provable properties of asymptotic safety in f(R) approximation

“…We show that we can impose square-integrability under the SL weight, in which case the valid operators are the ones that decay asymptotically like the inverse SL weight. We compute their asymptotic scaling dimensions, and we see that these operators are f (R)-analogues of the δ [45][46][47][48][49][50] as an alternative quantisation of quantum gravity.…”

“…This was first demonstrated in scalar field theory [44], while the tight theoretical structure that SL theory provides, lies behind the novel quantisation of gravity developed in refs. [45][46][47][48][49][50]. In ref.…”

“…We recognise that these are f (R)-approximation analogues of the δ (n) k (ϕ) operators introduced in [45] and studied extensively in refs. [46][47][48][49][50] as elements of a new quantisation of quantum gravity. Indeed the δ (n) k (ϕ) operators are eigenoperators appearing in the functional RG when using a wrong-sign cutoff (c h < 0), where it is needed because the conformal factor field, ϕ, has wrong-sign kinetic term.…”

“…In this case, by choosing to keep only interactions square integrable under the SL measure, the eigenoperator spectrum is again quantised, with v(R) ∼ 1/ω(R) for large R. These form a tower of operators, only finitely many of which are irrelevant, and infinitely many are relevant with dimensions given by minus the θ n in (6.1). These are the f (R)-approximation analogues of the δ (n) k (ϕ) operators pursued in [45][46][47][48][49][50] as an alternative quantisation of quantum gravity.…”

Editorial: Coarse graining in quantum gravity -- Bridging the gap between microscopic models and spacetime physics

“…Future perspectives: We consider the confluence of quantum-gravity approaches at this RG-vantage point a promising research area that is still in its relatively early stages. Promising ideas that have partially been substantiated in proof-of-principle papers within simplified settings include, e.g., i) the connection to phenomenology, that relies explicitly on the micro-to macro-connection encoded in the RG point of view, see, e.g., [26,27,28,29] and references therein, ii) the relation between approaches as members of the same universality class could enable an agreement on physical predictions arising from mathematically distinct frameworks, see, e.g., [30,31,32,33,34,35] and references therein, iii) the restoration of symmetries that are at the heart of the modern understanding of gravity, namely diffeomorphism symmetry and local Lorentz symmetry that could be recovered in the continuum limit, see, e.g., [36,37,38,39] and references therein, even though some approaches break these symmetries at intermediate stages of the construction.…”