Ponente
Descripción
A particular goal of holography is to understand the emergence of bulk geometry from the boundary conformal field theory. One geometrical application of entanglement is an auxiliary space for holography known as kinematic space—the space of pairs of CFT points. It is possible to define a parallel transport of modular Hamiltonians, which in turn, defines a Berry connection on kinematic space that reconstructs curves in the bulk. In this talk, I will introduce a new class of modular parallel transport governed by a change of global state. In this novel framework, the expectation value of the modular Berry curvature agrees with an appropriately defined bulk symplectic form associated with the entanglement wedge. Moreover, it is possible to define a quantum information metric on the space of density matrices from the Berry curvature, which is related to the canonical energy in the bulk. Time permitting, I will also discuss recent work on the kinematic space of holographic entropy inequalities and a novel two-sided Crofton formula to reconstruct spacetime.
