On the reconstruction problem in quantum gravity
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Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed point of the renormalization group flow, respectively. While it is clear that there should be a connection between these ingredients, their relation is far from trivial. This results in the so-called reconstruction problem. In this work, we demonstrate that the map between these two formulations does not generate non-localities at quadratic order in the background curvature. At this level, the bare action in the path integral and the fixed-point action obtained from the Wilsonian renormalization group differ by local terms only. This conclusion does not apply to theories coming with a physical ultraviolet cutoff or a fundamental non-locality scale.
| Original language | English |
|---|---|
| Article number | 137399 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 834 |
| ISSN | 0370-2693 |
| DOIs | |
| Publication status | Published - 10 Nov 2022 |
Bibliographical note
Funding Information:
The authors would like to thank B. Knorr for interesting discussions. A.P. acknowledges support by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. A.P. is also grateful to the Radboud University for hospitality during various stages of this project.
Funding Information:
The authors would like to thank B. Knorr for interesting discussions. A.P. acknowledges support by Perimeter Institute for Theoretical Physics . Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. A.P. is also grateful to the Radboud University for hospitality during various stages of this project.
Publisher Copyright:
© 2022 The Author(s)
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