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 $\hslash$. 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.

arXiv comment47 pages, 2 figures; Expanded version including discussion section. Version to be publ in JHEP

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• Provable properties of asymptotic safety in $f(R)$ approximation
• On the ultraviolet behavior of conformally reduced quadratic gravity
• The continuum limit of quantum gravity at second order in perturbation theory
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