Counter-term charges generate bulk symmetries

TL;DR

This paper demonstrates that counter-term charges in asymptotically AdS spacetimes generate the correct bulk symmetries and differ from other definitions only by boundary-dependent functions, using the Peierls bracket.

Contribution

It proves that counter-term charges produce the expected asymptotic symmetries and extends the construction to include non-vanishing boundary fields.

Findings

Counter-term charges generate the correct asymptotic symmetries.

Charges differ from other definitions by boundary-dependent functions.

The method applies even for boundary conformal symmetries.

Abstract

We further explore the counter-term 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 spaces and their kin. In particular, we show in general that charges defined via the counter-term 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 non-dynamical 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 counter-term subtraction construction of charges to the case in which additional non-vanishing boundary fields are present.