A generalized model for two dimensional quantum gravity and dynamics of random surfaces for d>1

TL;DR

This paper introduces a new continuum model for two-dimensional quantum gravity with matter central charge greater than one, which can describe smooth random surfaces in higher-dimensional flat space and matches recent numerical findings.

Contribution

It presents a generalized model for 2D quantum gravity applicable for d>1, incorporating symmetries and deriving critical exponents consistent with numerical results.

Findings

Effective field theory in low energy expansion

Model describes smooth self-avoiding random surfaces in d-dimensional space

Critical exponents align with recent numerical data

Abstract

The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we note that an effective field theory is achieved in low energy (large area) expansion, that may represent smooth self-avoiding random surfaces embedded in a $d$-dimensional flat space-time for arbitrary $d$. Moreover the values of some critical exponents are computed, that are in agreement with some recent numerical results.