Counterterm charges generate bulk 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.

Note on counterterms in asymptotically flat spacetimes

“…In general, different counterterms can lead to different results when computing the energy and the total action, seriously constraining the various choices of the boundary counterterms (see for instance [29,30] for a general study of the counterterm charges and a comparison with charges computed by other means in AdS context). While it is clear that the distinct choices of counterterms yield the same mass and action for the asymptotically flat spaces considered here, some of the components of the boundary stress-energy tensors obtained using various counterterms have slightly different coefficients (for example compare the second equations in (24) and (26) respectively; alternatively, see the stress-energy components computed for the Kaluza-Klein monopole in [13] using different counterterms).…”

Conformal Gravity Holography in Four Dimensions

“…where h is the metric on C and u i is the future-pointing unit vector normal to C. The combination of τ ij , P ij , and γ ð1Þ ij appearing in J i is precisely the modified stress tensor of Hollands et al [41]. Thus, the charges Eq.…”

Gravitation from entanglement in holographic CFTs

“…The reason is that a necessary first step in holographic renormalization is to render the variational principle at the spacetime boundary well-defined, and this can be rather difficult in a general higher derivative gravity theory (e.g. [52,53]). …”