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

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.

Automated summary

The proposal suggests including a new class of topologies in the path integral of three-dimensional pure gravity to address negative aspects in the spectrum, leading to a nonperturbative shift of the BTZ extremality bound. A two-dimensional calculation using dimensionally reduced theory can capture the primary effects in the near extremal limit, as demonstrated through a study of a related two-dimensional theory of Jackiw-Teitelboim gravity with dynamic defects, which is shown to be equivalent to a matrix integral.