Abstract
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton’s constant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).
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Acknowledgments
The author wishes to thank Hermann Nicolai, Stefan Theisen and the Max Planck Institut für Gravitationsphysik (Albert-Einstein-Institut) in Potsdam for a very warm hospitality. This work was supported in part by the Max Planck Gesellschaft zur Förderung der Wissenschaften.
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Invited lecture presented at the conference “Quantum Gravity: Challenges and Perspectives”, Bad Honnef, 14–16 April 2008. To appear in the proceedings edited by Hermann Nicolai.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hamber, H.W. Quantum gravity on the lattice. Gen Relativ Gravit 41, 817–876 (2009). https://doi.org/10.1007/s10714-009-0769-y
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DOI: https://doi.org/10.1007/s10714-009-0769-y