Numerical Study of c>1 Matter Coupled to Quantum Gravity

TL;DR

This paper uses numerical simulations to explore the c>1 barrier in 2D quantum gravity, analyzing Ising models on dynamical graphs and revealing universality linked to the central charge.

Contribution

It provides new numerical insights into the c>1 barrier by studying Ising models on dynamical graphs and analyzing fluctuations around mean field solutions.

Findings

Universality in graph properties determined by central charge

Behavior of moments of graph loop distribution analyzed

Qualitative understanding from fluctuations around mean field

Abstract

We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $\phi^3$ graphs and analyse the behaviour of moments of the graph loop distribution. We notice a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector.