Edge modes and Surface-Preserving Symmetries in Einstein-Maxwell Theory

Understand

Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations.

• We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation.
• We show that symplectic potential, which is defined in covariant phase space method, is not invariant under combined transformations.
• In order to deal with that problem, following Donnelly and Freidel proposal \cite{1}, we introduce new fields.