Title: State-Changing Modular Berry Phases
Abstract: I will describe the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In two dimensions this arises from the action of suitable diffeomorphisms on the circle. In general dimensions, it comes from deforming states that are prepared by the Euclidean path integral. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit. I will show that its bulk dual is an appropriately defined bulk symplectic form. We will compare with related results in the literature that use different definitions of parallel transport, and also highlight the distinctions between two and higher dimensions.
