12514 1804.01081 10.1007/JHEP02(2020)177 177 177 The factorization problem in Jackiw-Teitelboim gravity Regular Article - Theoretical Physics 1 32 2020 2 27 2019 11 14 2020 2 12 2020 2 27 The Author(s) 2021 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2020 2020 2 2 Daniel Harlow harlow@mit.edu Daniel Jafferis jafferis@physics.harvard.edu grid.116068.8 0000 0001 2341 2786 Center for Theoretical Physics Massachusetts Institute of Technology Cambridge MA 02138 USA grid.38142.3c 000000041936754X Center for the Fundamental Laws of Nature Harvard University Cambridge MA 02138 USA 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. Keywords 2D Gravity AdS-CFT Correspondence Black Holes ArXiv ePrint: 1804.01081