Counter-term charges generate bulk symmetries

TL;DR

The paper proves that charges defined by the counter-term subtraction method in asymptotically AdS spacetimes generate the correct bulk asymptotic symmetries via the covariant Peierls bracket. It shows that these charges can differ from Hamiltonian charges only by a function of boundary data (independent of bulk dynamics), and that this holds even when the boundary fields are non-scalar or when the asymptotic symmetry acts only conformally on the boundary. The authors extend the construction to broader asymptotic behaviors and boundary fields, providing a framework consistent with covariant phase-space methods and applicable to non-conformal gauge/gravity duals. Overall, the work clarifies the relationship between holographic charges, boundary data, and bulk symmetries, reinforcing the robustness of the counter-term approach in AdS/CFT contexts.

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.