The factorization problem in Jackiw-Teitelboim gravity
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13130_2020_Article_12514.pdf
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Author(s)
Harlow, Daniel L.
Jafferis, Daniel
Date Issued
February 2020
Journal
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Citation
Harlow, Daniel and Daniel Jafferis. "The factorization problem in Jackiw-Teitelboim gravity." Journal of High Energy Physics 2020, 2 (February 2020): 177 © 2020 The Authors
Version
Final published version
Abstract
In this note we study the 1 + 1 dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle-Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in 2 + 1 dimensions, which we’d then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP02(2020)177
