Counterterm charges generate bulk symmetries

We further explore the counterterm subtraction definition of charges (e.g., energy) for classical gravitating theories in spacetimes of relevance to gauge/gravity dualities; i.e., in asymptotically anti-de Sitter (AdS) spaces and their kin. In particular, we show in general that charges defined via the counterterm subtraction method generate the desired asymptotic symmetries. As a result, they can differ from any other such charges, such as those defined by bulk spacetime-covariant techniques, only by a function of auxiliary nondynamical structures such as a choice of conformal frame at infinity (i.e., a function of the boundary fields alone). Our argument is based on the Peierls bracket, and in the AdS context allows us to demonstrate the above result even for asymptotic symmetries which generate only conformal symmetries of the boundary (in the chosen conformal frame). We also generalize the counterterm subtraction construction of charges to the case in which additional nonvanishing boundary fields are present.