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- W3212413349 abstract "A bstract 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 n th eigenoperator, is λ n ∝ 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." @default.
- W3212413349 created "2021-11-22" @default.
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- W3212413349 date "2022-01-01" @default.
- W3212413349 modified "2023-09-27" @default.
- W3212413349 title "Provable properties of asymptotic safety in f(R) approximation" @default.
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- W3212413349 doi "https://doi.org/10.1007/jhep01(2022)041" @default.
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