  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.
