A continuum approach to 2D-Quantum Gravity for c$>$1

TL;DR

This paper develops a continuum model for 2D quantum gravity with matter central charge greater than one, modifying existing scaling laws and proposing models with real string tension applicable to various dimensions.

Contribution

It introduces a new continuum approach to 2D quantum gravity for c>1, modifying KPZ scaling and constructing models with real string tension.

Findings

Modified KPZ scaling for c>1

Models with real string tension for all c>1

Consistency with numerical results for d=3

Abstract

Two dimensional induced quantum gravity with matter central charge $c>1$ is studied taking a careful consideration of both diffeomorphism and Weyl symmetries . It is shown that, for the gauge fixing condition $R(g)$ (scalar curvature)=$const$, one obtains a modification of the David-Distler-Kawai version of KPZ scaling. We obtain a class of models with the real string tension for all values $c>1$. They contain an indeterminate parameter which is, however, strongly constrained by the requirement of non triviality of such a model. The possible physical significance of the new model is discussed. In particular we note that it describes smooth surfaces imbedded in $d$-dimensional flat space time for arbitrary $d$, consistently with recent numerical result for $d=3$.