Abstract: I will describe the parallel transport of modular Hamiltonians encoding entanglement properties of a state. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which differs appreciably from known Virasoro orbits. I will show that the boundary parallel transport process computes a bulk symplectic form for a Euclidean geometry obtained from the backreaction of a cosmic brane, with Dirichlet boundary conditions at the location of the brane. This construction gives a definition for the symplectic form on an entanglement wedge.