Quantum gravity and the renormalization group

Abstract

This work seeks to address the problem of quantum gravity from the point of view ofthe renormalisation group. After the introduction of the needed concepts, it is seenthat a problem of quantum gravity that stems from the “conformal factor instability”,if the consequences are fully explored, can open the door to a rich phenomenology. Inparticular, it is seen that toric universes can be constrained to be highly symmetricwhen sufficiently small, which is potentially applicable to the initial conditions forinflation. The idea of regularising gravity via a supermanifold is covered, followingsimilar treatments of gauge theory in order to preserve the symmetry (diffeomorphisminvariance) at all points along the renormalization group flow. Furthermore, themachinery provided by the conformal factor instability provides us with a genuinelyperturbative theory of quantum gravity, which can be calculated to have the sameeffective action as one might expect, but the understanding of the QFT is verydifferent, with the Gaussian fixed point being defined “off space-time”.

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ORCID for Matthew Peter Kellett: orcid.org/0000-0001-9573-4127

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