A solvable model of 3d quantum gravity

TL;DR

This paper introduces a solvable 3d quantum gravity model using multiple Virasoro TQFTs, demonstrating holographic duality, phase transitions, and resolving density of states negativity.

Contribution

It presents a new exactly solvable model of 3d quantum gravity with holographic duality and semiclassical features, including topology sums and phase transitions.

Findings

Matching bulk and boundary partition functions for small n

Large central charge limit yields semiclassical features

Inclusion of all topologies cures density of states negativity

Abstract

We consider a model of 3d quantum gravity defined by $n$ copies of a rational Virasoro TQFT with central charge $1/2$, summed over all 3d topologies. This theory is holographically dual to an ensemble of all 2d CFTs with central charge $c=n/2$ and chiral algebra that includes $Vir_{1/2}^n$. We perform the sum over topologies and evaluate the partition function of the bulk theory. We then confirm the holographic duality by matching it to the boundary ensemble for small $n$. We proceed to consider the limit of a large central charge, in which the bulk theory simplifies and condenses to an Abelian phase. In this regime, the model manifests many features expected in semiclassical 3d quantum gravity. In particular, inclusion of all 3d topologies in the bulk sum cures the negativity of the density of states evaluated by the torus partition function. The model also exhibits a Hawking-Page transition, an exponentially suppressed wormhole amplitude, and provides a toy example of the holographic code. We discuss these aspects in detail and conclude with lessons for semiclassical quantum gravity.