#### Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity

Journal of High Energy Physics
August 2018, 2018:24 | Cite as
Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
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Tim R. Morris
Open Access
Regular Article - Theoretical Physics
First Online: 07 August 2018
Received: 14 February 2018
Revised: 13 March 2018
Accepted: 27 July 2018
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Abstract
The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete flows exist only in the reverse direction (i.e. from the infrared to the ultraviolet). The Gaussian fixed point supports infinite sequences of composite eigenoperators of increasing infrared relevancy (increasingly negative mass dimension), which are orthonormal and complete for bare interactions that are square integrable under the appropriate measure. These eigenoperators are non-perturbative in ℏ and evanescent. For ℝ4 spacetime, each renormalized physical operator exists but only has support at vanishing field amplitude. In the generic case of infinitely many non-vanishing couplings, if a complete RG flow exists, it is characterised in the infrared by a scale Λp > 0, beyond which the field amplitude is exponentially suppressed. On other spacetimes, of length scale L, the flow ceases to exist once a certain universal measure of inhomogeneity exceeds O(1) + 2πL2Λ p 2 . Importantly for cosmology, the minimum size of the universe is thus tied to the degree of inhomogeneity, with space-times of vanishing size being required to be almost homogeneous. We initiate a study of this exotic quantum field theory at the interacting level, and discuss what the full theory of quantum gravity should look like, one which must thus be perturbatively renormalizable in Newton’s constant but non-perturbative in ℏ.
Keywords Models of Quantum Gravity Renormalization Group Renormalization Regularization and Renormalons
ArXiv ePrint: 1802.04281
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© The Author(s) 2018
Authors and Affiliations
Tim R. Morris1Email authorView author's OrcID profile1.STAG Research Centre & Department of Physics and AstronomyUniversity of SouthamptonSouthamptonU.K.