General dilatonic gravity with an asymptotically free gravitational coupling constant near two dimensions

TL;DR

This paper investigates a renormalizable dilatonic gravity theory near two dimensions, demonstrating the existence of a non-trivial ultraviolet fixed point with an asymptotically free gravitational coupling, and explores related models and fermionic extensions.

Contribution

It introduces a general renormalizable dilatonic gravity model with a kinetic dilaton term, proves the existence of a non-trivial UV fixed point, and compares it with related models at the quantum level.

Findings

Existence of a non-trivial ultraviolet fixed point.

Asymptotically free gravitational coupling near two dimensions.

Distinction between Jackiw-Teitelboim and lineal gravity at quantum level.

Abstract

We study a renormalizable, general theory of dilatonic gravity (with a kinetic-like term for the dilaton) interacting with scalar matter near two dimensions. The one-loop effective action and the beta functions for this general theory are written down. It is proven that the theory possesses a non-trivial ultraviolet fixed point which yields an asymptotically free gravitational coupling constant (at $\epsilon \rightarrow 0$) in this regime. Moreover, at the fixed point the theory can be cast under the form of a string-inspired model with free scalar matter. The renormalization of the Jackiw-Teitelboim model and of lineal gravity in $2+\epsilon$ dimensions is also discussed. We show that these two theories are distinguished at the quantum level. Finally, fermion-dilatonic gravity near two dimensions is considered.