Remarks on the origin of almost-Gaussian scaling in asymptotically safe quantum gravity

The gravitational asymptotic safety program envisions the high-energy completion of gravity through an interacting renormalization group fixed point, the Reuter fixed point. The predictive power of the construction is encoded in the spectrum of the stability matrix which is obtained from linearizing the renormalization group flow around this fixed point. A key result of the asymptotic safety program is that parts of this spectrum exhibit an almost-Gaussian scaling behavior, entailing that operators which are classically highly UV irrelevant do not induce new free parameters. In this article, we track down the origin of this property by contrasting the structure of the stability matrix computed from the Wetterich equation and the composite-operator equation within the realm of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>f</a:mi><a:mo stretchy="false">(</a:mo><a:mi>R</a:mi><a:mo stretchy="false">)</a:mo></a:math> truncations. We show that the almost-Gaussian scaling is not linked to the classical part of the beta functions. It is a quantum-induced almost-Gaussian scaling originating from the quantum corrections in the flow equation. It relies on a subtle interplay among the analytic structure of the theory’s two-point function and the way the Wetterich equation integrates out fluctuation modes. As a byproduct we determine the parts of the eigenmode spectrum that is robust with respect to changing the regularization procedure. Published by the American Physical Society 2024