The factorization problem in Jackiw-Teitelboim gravity
By D. Harlow, D. Jafferis. Journal of High Energy Physics, 2018
221 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/38b424634345ed759ad578760846d3ee28738552
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Citations in the corpus
- JT gravity and the ensembles of random matrix theory (2019, background): “The contribution of a particular topology to the path (1)This has included many different derivations of the exact path integral [12, 13, 14, 15, 16, 17, 18, 19, 20], studies of the Hilbert space structure [21, 18, 22, 23], correlation functions [24, 25, 26], the physical symmetry charges [27], and ”
- Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “We may define |HHβ〉 by its matrix elements in the length basis [21, 41], with 〈`|HHβ〉 ≡ ψD,β/2(`) equal to the integral over all Euclidean geometries with the topology of a disk and boundary consisting of an asympotically AdS portion of renormalized length β/2 and a geodesic portion of renormalized ”
- JT gravity as a matrix integral (2019, background): “Several studies have pointed to the importance in JT gravity of surfaces of other topologies [11, 12, 13].”
- An algebra of observables for de Sitter space (2022, background): “Nevertheless, JT gravity has a two-dimensional phase space, which was analyzed in detail in [52], for example.”
- A semiclassical ramp in SYK and in gravity (2018, background): “The implications of the existence of wormholes in JT gravity for factorization has been discussed in [31].”
- The quantum gravity dynamics of near extremal black holes (2018, methodology): “-DeWitt Wavefunction In the pure JT theory we can think about quantizing the bulk theory and obtaining the Wheeler-DeWitt wavefunction. This was discussed in the classical limit by Harlow and Jaeris [10]. The Wheeler-DeWitt wavefunction can be created by Euclidean evolution of the boundary and hence”
- Replica wormholes and the black hole interior (2019, background): “29) is the Hartle-Hawking state in the geodesic basis [51].”
- Inconsistency of islands in theories with long-range gravity (2021, background): “Moreover [118], extending the techniques of [119, 120], analyzed the significance of the bulk constraints in pure JT gravity without matter and showed that these constraints prevent the factorization of the Hilbert space on the boundary, which is a puzzle that is somewhat similar in flavor to the pu”