The unitary conformal field theory behind 2D Asymptotic Safety

TL;DR

This paper explores a 2D conformal field theory emerging from asymptotic safety in quantum gravity, revealing a unitary fixed point with a non-local effective action and implications for 2D quantum gravity models.

Contribution

It constructs a 2D limit of the asymptotic safety flow, identifying a unitary CFT with positive central charge and analyzing its properties and implications for quantum gravity.

Findings

Identifies a nontrivial fixed point with a unitary CFT in 2D asymptotic safety.

Shows the fixed point corresponds to a Liouville theory with positive central charge c=25.

Discovers a mechanism that quenches KPZ scaling in 2D asymptotically safe gravity.

Abstract

Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in $d>2$ dimensions and Polyakov's induced gravity action in two dimensions.