The gravitational dynamics of kinematic space

Abstract

We show that the dynamics of the kinematic space of a 2-dimensional CFT is gravitational and described by Jackiw-Teitelboim theory. We discuss the first law of this 2-dimensional dilaton gravity theory to support the relation between modular Hamiltonian and dilaton that underlies the kinematic space construction. It is further argued that Jackiw-Teitelboim gravity can be derived from a 2-dimensional version of Jacobson's maximal vacuum entanglement hypothesis.

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…Also, similar to the work of [85], we conjecture that the dynamics of the kinematic space for warped CFTs would be the dynamics of the two-dimensional chiral Liouville gravity, which would be the corresponding deformed version of Jackiw-Teitelboim (JT) gravity. In this case however, as shown in [22], the throats of WAdS 3 with a finite volume of spatial circle would not completely decouple from the rest of the geometry.…”

“…In [85], the gravitational dynamics of kinematic space have been discussed and there it has been argued that it could be described by the "Jackiw-Teitelboim" gravity theory. The relationship between the modular Hamiltonian and the dilaton in the gravity model which underlies the kinematic space construction has been discussed.…”

Defects in Jackiw-Teitelboim quantum gravity

“…The metric (4.4) describes a Liouville worldsheet metric with a local puncture, interpreted as a conical deficit in JT gravity. The fact that the gravitational bulk carries the Liouville metric identifies the bulk as the kinematic space of the boundary Schwarzian [32,60,61]. The total energy T (τ ) of this configuration is Path-integrating Φ results in the constraint R(x) = −2 + α16πGδ(x − y), which is AdS 2 space with a conical singularity at the prescribed point y.…”

Entanglement entropy of two coupled SYK models and eternal traversable wormhole

“…From this point of view, the Bekenstein Hawking entropy of near-extremal black holes was interpreted in the context of AdS 2 /CFT 1 correspondence [14,15,16,17], and was related to entanglement entropy via the RT formula in [18]. There are also other recent progress in understanding entanglement entropy in AdS 2 gravity from different perspectives [19,20,21,22].…”