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 higher-dimensional terms and identifying a stable ultraviolet fixed point for the Einstein constant beyond two dimensions.

Contribution

It introduces the concept of quantum reparametrizations in 2D gravity and links them to $2+ ext{epsilon}$ dimensional terms, providing new insights into the theory's structure.

Findings

Quantum reparametrizations are equivalent to $2+ ext{epsilon}$-dimensional terms.

The $eta$-function for the Einstein constant has a non-trivial ultraviolet stable point.

The structure of one-loop counterterms in 2D gravity is clarified.

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.