Provable properties of asymptotic safety in f(R) approximation
Provable properties of asymptotic safety in f(R) approximation
We study an f(R) approximation to asymptotic safety, using a family of non-adaptive cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global fixed point solution and its eigenoperators. For this family of cutoffs, the scaling dimension at large n of the nth eigenoperator, is λn ∝ b n ln n. The coefficient b is non-universal, a consequence of the single-metric approximation. The large R limit is universal on the hyperboloid, but not on the sphere where cutoff dependence results from certain zero modes. For right-sign conformal mode cutoff, the fixed points form at most a discrete set. The eigenoperator spectrum is quantised. They are square integrable under the Sturm-Liouville weight. For wrong sign cutoff, the fixed points form a continuum, and so do the eigenoperators unless we impose square-integrability. If we do this, we get a discrete tower of operators, infinitely many of which are relevant. These are f(R) analogues of novel operators in the conformal sector which were used recently to furnish an alternative quantisation of gravity.
Models of Quantum Gravity, Nonperturbative Effects, Renormalization Group
Mitchell, Alex
068b4348-a75e-45da-a582-65c866bb95ab
Morris, Timothy
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Stulga, Dalius
3ea3b0d0-26a0-45aa-bd83-8437daecfa95
11 January 2022
Mitchell, Alex
068b4348-a75e-45da-a582-65c866bb95ab
Morris, Timothy
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Stulga, Dalius
3ea3b0d0-26a0-45aa-bd83-8437daecfa95
Mitchell, Alex, Morris, Timothy and Stulga, Dalius
(2022)
Provable properties of asymptotic safety in f(R) approximation.
Journal of High Energy Physics, 2022 (1), [41].
(doi:10.1007/JHEP01(2022)041).
Abstract
We study an f(R) approximation to asymptotic safety, using a family of non-adaptive cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global fixed point solution and its eigenoperators. For this family of cutoffs, the scaling dimension at large n of the nth eigenoperator, is λn ∝ b n ln n. The coefficient b is non-universal, a consequence of the single-metric approximation. The large R limit is universal on the hyperboloid, but not on the sphere where cutoff dependence results from certain zero modes. For right-sign conformal mode cutoff, the fixed points form at most a discrete set. The eigenoperator spectrum is quantised. They are square integrable under the Sturm-Liouville weight. For wrong sign cutoff, the fixed points form a continuum, and so do the eigenoperators unless we impose square-integrability. If we do this, we get a discrete tower of operators, infinitely many of which are relevant. These are f(R) analogues of novel operators in the conformal sector which were used recently to furnish an alternative quantisation of gravity.
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2111.05067
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Mitchell2022_Article_ProvablePropertiesOFAsymptotic
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Accepted/In Press date: 27 December 2021
Published date: 11 January 2022
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© 2022, The Author(s).
Keywords:
Models of Quantum Gravity, Nonperturbative Effects, Renormalization Group
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Local EPrints ID: 455173
URI: http://eprints.soton.ac.uk/id/eprint/455173
ISSN: 1029-8479
PURE UUID: 3451c25c-f876-482d-988c-7b84557d7c6c
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Date deposited: 11 Mar 2022 17:41
Last modified: 17 Mar 2024 02:34
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Author:
Alex Mitchell
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