Off-shell divergences in quantum gravity
Off-shell divergences in quantum gravity
We investigate off-shell perturbative renormalisation of pure quantum gravity for both background metric and quantum fluctuations. We show that at each new loop order, the divergences that do not vanish on-shell are constructed from only the total metric, whilst those that vanish on-shell are renormalised by canonical transformations involving the quantum fields. Purely background metric divergences do not separately appear, and the background metric does not get renormalised. We highlight that renormalisation group identities play a crucial role ensuring consistency in the renormalisation of BRST transformations beyond one loop order. We verify these assertions by computing leading off-shell divergences to two loops, exploiting off-shell BRST invariance and the renormalisation group equations. Although some divergences can be absorbed by field redefinitions, we explain why this does not lead to finite beta-functions for the corresponding field.
hep-th, gr-qc
Mandric, Vlad-Mihai
04dbbef5-4c78-4ab4-8e0f-ed2c86554c14
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Stulga, Dalius
3ea3b0d0-26a0-45aa-bd83-8437daecfa95
14 August 2023
Mandric, Vlad-Mihai
04dbbef5-4c78-4ab4-8e0f-ed2c86554c14
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Stulga, Dalius
3ea3b0d0-26a0-45aa-bd83-8437daecfa95
[Unknown type: UNSPECIFIED]
Abstract
We investigate off-shell perturbative renormalisation of pure quantum gravity for both background metric and quantum fluctuations. We show that at each new loop order, the divergences that do not vanish on-shell are constructed from only the total metric, whilst those that vanish on-shell are renormalised by canonical transformations involving the quantum fields. Purely background metric divergences do not separately appear, and the background metric does not get renormalised. We highlight that renormalisation group identities play a crucial role ensuring consistency in the renormalisation of BRST transformations beyond one loop order. We verify these assertions by computing leading off-shell divergences to two loops, exploiting off-shell BRST invariance and the renormalisation group equations. Although some divergences can be absorbed by field redefinitions, we explain why this does not lead to finite beta-functions for the corresponding field.
Text
2308.07382v1
- Author's Original
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Published date: 14 August 2023
Keywords:
hep-th, gr-qc
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Local EPrints ID: 481574
URI: http://eprints.soton.ac.uk/id/eprint/481574
PURE UUID: 363f273c-495a-481c-a8c3-2a16eec40162
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Date deposited: 04 Sep 2023 16:37
Last modified: 18 Mar 2024 03:53
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