The gravitational dynamics of kinematic space

TL;DR

This paper demonstrates that the dynamics of kinematic space in 2D CFTs is governed by Jackiw-Teitelboim gravity, linking entanglement, modular Hamiltonian, and gravitational theories in a novel way.

Contribution

It establishes a gravitational description of kinematic space via JT gravity and derives this from a maximal vacuum entanglement principle, connecting boundary CFTs to bulk gravity.

Findings

Kinematic space dynamics are described by Jackiw-Teitelboim gravity.

The relation between modular Hamiltonian and dilaton supports the gravitational interpretation.

Coupling boundary CFT to JT gravity via entanglement yields the 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. Applied to the kinematic space context, this leads us to the statement that the kinematic space of a 2-dimensional boundary CFT can be obtained from coupling the boundary CFT to JT gravity through a maximal vacuum entanglement principle.