The true Quantum Metric of Quantum Gravity
Final Report Abstract
Our understanding of nature on the currently most fundamental level rests on the two cornerstones of Einstein’s general relativity, as the dynamical theory of gravitation, and quantum field theory describing all known matter particles and their microscopic interactions. It is a puzzling and challenging circumstance that both theory concepts seem mutually incompatible; this observation is made at least on the method level of perturbative expansions about weak coupling where Einstein’s theory appears to be inconsistent with standard quantization recipes. Many candidate scenarios have been developed over the past decades to construct a unified and predictive framework for both theory cornerstones. Recent years have seen remarkable progress of the scenario of asymptotically safe quantum gravity in which gravity is treated as a fundamental quantum field theory the quantization of which, however, needs to be performed beyond the weak coupling region. The methods and perspectives required for this quantization of gravity have matured over the past years often drawing heavily on quantization of strongly correlated systems or critical phenomena as encountered in a variety of systems of many-body physics, particle physics or statistical mechanics; these methods are summarized under the name of renormalization theory. Still, decisive questions intricately related to the nature of Einstein’s theory have remained unsovled so far. Among them, the quest for the true metric of quantum gravity or, more precisely, the question of background independence of asymptotically safe quantum gravity. The present project has been devoted to this essential problem, as the metric is the object in Einstein’s theory that carries the dynamical degrees of freedom. The most important result of the proposal has been the exploration of the renormalization of metric gravity with an Einstein-Hilbert-type action in d = 2 + ε dimensions with the intent of framing the discussion on the four-dimensional asymptotic safety conjecture from a different angle. The aim has been to develop a framework that is reliable and systematic as perturbative expansions, but nevertheless gives benchmark limits for nonperturbative computations based instead on functional renormalization group methods that are carried out directly in d = 4. Several lessons can be drawn from the proposal’s results, which are expected to become of relevance for the future of the asymptotic safety approach to quantum gravity. The most important lesson is that it is necessary to go on-shell, i.e., to satify the equations of motion, in order to have gauge and parametrization independence going forward in the development of the approach. The project has demonstrated explicitly how the true metric can be constructed in our expansion scheme, and showed how to resolve a discrepancy of seminal literature results in d = 2 + ε-dimensional gravity using a careful symmetry analysis. A novel result of the proposal is the development of a dimensional regularization scheme for quantum gravity which keeps the dependence on spacetime’s dimension in the counterterms of the Feynman diagrams as a parameter. This approach was pivotal for drawing another important lesson of the proposal: there appears to be an effective upper critical dimension for the continued theory above two dimensions (e.g. in d = 2 + ε for ε > 0). Remarkably, the upper critical dimension is estimated to be bigger than four, confirming the hypothesis of asymptotic safety at the physical dimension of spacetime.
Publications
- Renormalization of multicritical scalar models in curved space, Eur. Phys. J. C 79 (2019) no.3, 203
R. Martini and O. Zanusso
(See online at https://doi.org/10.1140/epjc/s10052-019-6721-8) - Fractal Geometry of Higher Derivative Gravity, Phys. Rev. Lett. 124 (2020) no.15, 151302
M. Becker, C. Pagani and O. Zanusso
(See online at https://doi.org/10.1103/physrevlett.124.151302) - Gravity in d = 2 + ε dimensions and realizations of the diffeomorphisms group, Eur. Phys. J. C 81 (2021), 916
R. Martini, A. Ugolotti, F. Del Porro and O. Zanusso
(See online at https://doi.org/10.1140/epjc/s10052-021-09719-z) - The Search for the Universality Class of Metric Quantum Gravity, Universe 7 (2021) no.6, 162
R. Martini, A. Ugolotti and O. Zanusso
(See online at https://doi.org/10.3390/universe7060162)
