A new perspective on matter coupling in 2d quantum gravity

TL;DR

This paper demonstrates that a non-perturbative 2D Lorentzian quantum gravity model coupled with Ising spins behaves like flat space, supported by analytical and simulation evidence, suggesting it as a smooth alternative to Liouville quantum gravity.

Contribution

It provides the first comprehensive evidence that Lorentzian quantum gravity coupled with matter exhibits flat-space behavior, contrasting with traditional Liouville models.

Findings

High-temperature expansion confirms flat-space behavior.

Monte Carlo simulations support the weak-coupling regime.

The model shows a smoother critical behavior than Liouville quantum gravity.

Abstract

We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much `smoother' critical behaviour.