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Status of the Asymptotic Safety Paradigm for Quantum Gravity and Matter

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Abstract

In the asymptotic safety paradigm, a quantum field theory reaches a regime with quantum scale invariance in the ultraviolet, which is described by an interacting fixed point of the Renormalization Group. Compelling hints for the viability of asymptotic safety in quantum gravity exist, mainly obtained from applications of the functional Renormalization Group. The impact of asymptotically safe quantum fluctuations of gravity at and beyond the Planck scale could at the same time induce an ultraviolet completion for the Standard Model of particle physics with high predictive power.

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Notes

  1. In approaches to quantum gravity that focus on a “pre-geometric” phase, where a continuum spacetime is yet to emerge from underlying discrete building blocks, the RG can be set up in a more abstract way, by coarse-graining from many to few degrees of freedom, but this typically also appears to imply the breaking of a symmetry of the model, see, e.g., [53].

  2. The fixed point in \(d=4\) might of course not be smoothly connected to that in \(d=2+\epsilon \), but a smooth connection to a perturbative regime provides another powerful tool to characterize the fixed point. Moreover, for a fixed point in \(d=4\) that smoothly connects to one in \(d=2\), the scaling exponents are given by canonical scaling dimensions plus terms which go to zero as \(\epsilon \rightarrow 2\). These additional terms might be quantitatively small in \(d=4\), and the fixed point could inherit a close-to-canonical scaling behavior. This is an excellent basis to set up truncations that show apparent convergence.

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Acknowledgements

I thank the organizers of the workshop on Black Holes, Gravitational Waves and Spacetime Singularities for the invitation to a particularly inspiring workshop. It is a pleasure to thank N. Christiansen, P. Donà, H. Gies, A. Held, P. Labus, S. Lippoldt, J. Pawlowski, R. Percacci, M. Reichert and F. Versteegen for enjoyable and fruitful collaborations on gravity-matter systems, some part of which is reflected in these notes. I am indebted to A. Held and F. Versteegen for help in making this summary (hopefully) more understandable. I acknowledge funding by the DFG within the Emmy–Noether-program under grant no. Ei-1037-1 and support by the Perimeter Institute for Theoretical Physics through the Emmy–Noether-visiting fellow program.

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  1. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany

    Astrid Eichhorn

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Eichhorn, A. Status of the Asymptotic Safety Paradigm for Quantum Gravity and Matter. Found Phys 48, 1407–1429 (2018). https://doi.org/10.1007/s10701-018-0196-6

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