Bottleneck Surfaces and Worldsheet Geometry of Higher-Curvature Quantum Gravity

TL;DR

This paper introduces a lattice model for higher-curvature quantum gravity in two dimensions, analyzing its phase structure and revealing entropic instability and branched polymer behavior near phase transitions.

Contribution

It presents a simple lattice framework for higher-curvature quantum gravity and investigates its phase behavior, highlighting entropic instabilities and geometric transitions.

Findings

Flat graphs are entropically unstable to baby universe formation

Graph growth shows branched polymer behavior before flattening transition

Phase structure depends on curvature coupling

Abstract

We describe a simple lattice model of higher-curvature quantum gravity in two dimensions and study the phase structure of the theory as a function of the curvature coupling. It is shown that the ensemble of flat graphs is entropically unstable to the formation of baby universes. In these simplified models the growth in graphs exhibits a branched polymer behaviour in the phase directly before the flattening transition.