  We study the parallel transport of modular Hamiltonians encoding entanglement
properties of a state. In the case of 2d CFT, we consider a change of state
through action with a suitable diffeomorphism on the circle: one that
diagonalizes the adjoint action of the modular Hamiltonian. These vector fields
exhibit kinks at the interval boundary, thus together with their central
extension they differ from usual elements of the Virasoro algebra. 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. We find 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. We propose that this gives a
reasonable definition for the symplectic form on an entanglement wedge.
