The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral

TL;DR

This paper suggests including new topologies in 3D gravity path integrals to fix spectrum issues, using a 2D JT gravity model with defects that maps to a matrix integral, revealing nonperturbative effects near extremality.

Contribution

It introduces new topologies into 3D gravity path integrals and demonstrates their equivalence to a matrix model via a 2D JT gravity with defects, addressing spectrum pathologies.

Findings

Inclusion of new topologies resolves spectrum negativities.

2D JT gravity with defects maps to a matrix integral.

Nonperturbative shift of the extremality bound is identified.

Abstract

We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two-dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.