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.
Highlights
In the quest to understand quantum mechanical theories of gravity, one central problem is to distinguish low energy theories with consistent ultraviolet completions from those without
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 have proposed a mechanism to resolve this tension, by including certain topologies in the path integral for which there is no classical solution
Summary
In the quest to understand quantum mechanical theories of gravity, one central problem is to distinguish low energy theories with consistent ultraviolet completions from those without. A natural way to attempt to construct a quantum theory of pure gravity is by quantizing the classical theory, for example using a path integral over metrics, but it is very challenging to make sense of this in most cases. We can ameliorate these difficulties by studying low-dimensional models, in which gravity simplifies enough that we can hope for a more complete understanding. The path integral of JT gravity was recently solved exactly by Saad, Shenker and Stanford [8], and we draw heavily from their work Their main result was that JT gravity has a dual quantum mechanical description as a double-scaled matrix integral. We review the context of the paper and summarize our main results
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