Quantum Gravity and Random Geometry

Provable properties of asymptotic safety in f(R) approximation

17 janv. 2023, 10:50

50m

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Tim Morris (University of Southampton)

Description

We study an $f(R)$ approximation to asymptotic safety, using a family of 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 $n^{\text{th}}$ eigenoperator, is ${\lambda }_n\propto bn\ln n$. The coefficient $b$ is non-universal, a consequence of the single-metric approximation. 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, as required if starting from the Einstein-Hilbert action, 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.