Quantum reparametrizations in the two-dimensional gravity: a look from 2+$epsilon$ dimensions

TL;DR

This paper investigates quantum reparametrizations in 2D gravity, revealing their equivalence to 2+epsilon dimensional terms and identifying a non-trivial ultraviolet stable point for the Einstein constant.

Contribution

It demonstrates the connection between quantum reparametrizations and dimensional extensions, and analyzes the beta-function's fixed points in 2+epsilon dimensions.

Findings

Quantum reparametrizations are equivalent to 2+epsilon-dimensional terms.

The beta-function for the Einstein constant has a non-trivial UV stable point.

One-loop counterterms are characterized in the covariant scheme.

Abstract

We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations.Some of them are shown to be equivalent to the introduction of 2+$epsilon$-dimensional terms into the initially 2-dimensional theory. We also argue that the beta-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.