Scaling Exponents in Quantum Gravity near Two Dimensions

TL;DR

This paper investigates quantum gravity near two dimensions by explicitly separating the conformal mode, computing anomalous dimensions, and identifying an ultraviolet fixed point that depends on the central charge, with implications for the universe's phase structure.

Contribution

It introduces a formulation of quantum gravity in $2+ extepsilon$ dimensions that explicitly handles the conformal mode and reproduces known 2D scaling exponents in the strong coupling limit.

Findings

Reproduces 2D quantum gravity scaling exponents in the strong coupling limit.

Identifies an ultraviolet fixed point for $c<25$ separating phases.

Suggests the weak coupling phase may relate to our universe with massless gravitons.

Abstract

We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The renormalization of the gravitational dressed operators is studied and their anomalous dimensions are computed. The exact scaling exponents of the 2 dimensional quantum gravity are reproduced in the strong coupling regime when we take $\epsilon\rightarrow0$ limit. The theory possesses the ultraviolet fixed point as long as the central charge $c<25$, which separates weak and strong coupling phases. The weak coupling phase may represent the same universality class with our Universe in the sense that it contains massless gravitons if we extrapolate $\epsilon$ up to 2.