Towards a Unitary, Renormalizable, and Ultraviolet-Complete Quantum Theory of Gravity

Abstract

For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry that derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Hořava gravity, a quantum Lifshitz field theory of gravity characterized by an anisotropic scaling between space and time, unitarity and renormalizability can be retained while Lorentz invariance is sacrificed at high energies and must emerge only as approximate symmetry at low energies. This article reviews various approaches to perturbative quantum gravity, with a particular focus on recent progress in the quantization of Hořava gravity, supporting its theoretical status as a unitary, renormalizable, and ultraviolet-complete quantum theory of gravity.

Towards Black-Hole Singularity-Resolution in the Lorentzian Gravitational Path Integral

“…Fourth, changing the underlying symmetries in the path integral, e.g., to foliationpreserving diffeomorphisms, as, e.g., in Horava-Lifshitz gravity [91] (see [92] for a recent review), could require different invariants to be included for singularity-resolution. In this spirit, a comparison of diverse quantum-field-theoretic proposals for gravity which differ in (a) the underlying (gauge) symmetries and/or (b) the choice of fields, see, e.g., [93][94][95][96] for proposals which are classically equivalent to GR, could be illuminating.…”

The phase diagram of the multi-matrix model with ABAB interaction from functional renormalization

“…A possible way out of this issue is to replace the Einstein-Hilbert action by one which allows for a unitary and perturbatively renormalizable QFT. However, this might dispense with micro-causality as in the case of higher-derivative gravity [36][37][38] or with Lorentz invariance as in Hořava-Lifshitz gravity [39], see [40] for a recent review. An alternative pathway to quantize gravity within the continuum formulation of the path integral is explored by the asymptotic-safety program.…”

Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument

“…Indeed, most of the above treated modified theories of gravity might be not-renormalizable when more detailed aspects are considered, as well the propagator homogeneity in the momenta space [72]. Detailed discussions on the renormalizability of f (R) theories of gravity can be found e.g., in [73][74][75][76]. One of the first attempts towards a renormalization scheme was pursued by Stelle in [77].…”