Scaling exponents in quantum gravity near two dimensions

Abstract

We formulate quantum gravity in 2 + ϵ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of 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 two-dimensional quantum gravity are reproduced in the strong coupling regime when we take the ϵ → 0 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 ϵ up to 2.