Dynamical Edge Modes and Entanglement in Maxwell Theory

Understand

Previous work on black hole partition functions and entanglement entropy suggests the existence of "edge" degrees of freedom living on the (stretched) horizon.

• We identify a local and "shrinkable" boundary condition on the stretched horizon that gives rise to such degrees of freedom.
• They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate.
• Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split.