The Spectral Dimension of 2D Quantum Gravity

TL;DR

This paper demonstrates that the spectral dimension of 2D quantum gravity coupled with Gaussian fields remains two across all central charge values c <= 1, and also confirms the known spectral dimension of 4/3 for branched polymers.

Contribution

It provides a unified proof that the spectral dimension is two for 2D quantum gravity with Gaussian fields and reaffirms the spectral dimension for branched polymers.

Findings

Spectral dimension d_s=2 for 2D quantum gravity with Gaussian fields for c <= 1

Simple proof of d_s=4/3 for branched polymers

Unified approach to spectral dimensions in different models

Abstract

We show that the spectral dimension d_s of two-dimensional quantum gravity coupled to Gaussian fields is two for all values of the central charge c <= 1. The same arguments provide a simple proof of the known result d_s= 4/3 for branched polymers.