DILATONIC GRAVITY NEAR TWO DIMENSIONS AND ASYMPTOTIC FREEDOM OF THE GRAVITATIONAL COUPLING CONSTANT

TL;DR

This paper explores two models of dilatonic gravity near two dimensions, demonstrating they are renormalizable, possess a non-trivial ultraviolet fixed point, and exhibit asymptotic freedom of the gravitational coupling constant.

Contribution

It introduces and analyzes renormalizable dilatonic gravity models with asymptotic freedom and non-trivial fixed points in two dimensions.

Findings

Both models have a non-trivial ultraviolet fixed point.

The gravitational constant is asymptotically free at the fixed point.

Matter central charge can be increased significantly in the asymptotic freedom regime.

Abstract

Two models of dilatonic gravity are investigated: (i) dilaton-Yang-Mills gravity and (ii) higher-derivative dilatonic gravity. Both are renormalizable in $2+\epsilon$ dimensions and have a smooth limit for $\epsilon \rightarrow 0$. The corresponding one-loop effective actions and beta-functions are found. Both theories are shown to possess a non-trivial ultraviolet fixed point ---for all dilatonic couplings--- in which the gravitational constant is asymptotically free. It is shown that in the regime of asymptotic freedom the matter central charge can be significantly increased by two different mechanisms ---as compared with pure dilatonic gravity, where $n < 24$.