The true Quantum Metric of Quantum Gravity

• Applicant: Professor Dr. Holger Gies, since 6/2019
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 396639009

The construction of a quantum theory of gravity is a highly challenging open problem of theoretical physics. One promising candidate solution is asymptotically safe quantum gravity. According to the asymptotic safety conjecture, metric gravity can be completed at high energies by a suitable non-trivial interacting theory. On the one hand this resembles the ultraviolet completion of Yang-Mills theory in terms of asymptotic freedom, and on the other hand the high-energy theory exhibits features similar to quantum criticality of complex systems. Asymptotic safety provides a mechanism to construct a theory of quantum gravity that is predictive and naturally interpolates with general relativity at lower energies. In recent years, these properties have been extensively tested by applying the background field method, and were verified within any conceived approximation. This exciting development has left a severe open problem: the proof of background independence of the approach. The objective of this project is to clarify the notion of a true quantum metric, which is the background independent field of the quantum theory of gravity. The project proposes the non-perturbative generalization of two independent methods, previously developed for the perturbative quantization of non-linear sigma models, and their application to asymptotically safe gravity. The methods are based on the construction of generalized sources, which will be used to construct the true quantum metric. Strength and reliability of these new techniques will be tested through their application to the study of the O(N) universality class and the quantization of the non-linear sigma model in more than two dimensions. The true quantum metric can provide an elegant solution to a long standing problem, and has the potential to set a new standard for all future developments of asymptotic safety and/or metric quantum gravity.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Dr. Omar Zanusso, from 12/2017 until 5/2019