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- Title
Provable properties of asymptotic safety in f(R) approximation.
- Authors
Mitchell, Alex; Morris, Tim R.; Stulga, Dalius
- 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.
- Subjects
QUANTUM gravity; RENORMALIZATION group; GRAVITY; SAFETY
- Publication
Journal of High Energy Physics, 2022, Vol 2022, Issue 1, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP01(2022)041