Wald-Zoupas prescription with soft anomalies

We show that the Wald-Zoupas prescription for gravitational charges is valid in the presence of anomalies and field-dependent diffeomorphism, but only if these are related to one another in a specific way. The geometric interpretation of the allowed anomalies is exposed looking at the example of BMS symmetries; they correspond to soft terms in the charges. We determine if the Wald-Zoupas prescription coincides with an improved Noether charge. The necessary condition is a certain differential equation, and when it is satisfied, the boundary Lagrangian of the resulting improved Noether charge contains, in general, a nontrivial corner term that can be identified a priori from a condition of anomaly freeness. Our results explain why the Wald-Zoupas prescription works in spite of the anomalous behavior of BMS trans-formations, and should be helpful to relate different branches of the literature on surface charges.

Automated summary

We demonstrate the validity of the Wald-Zoupas prescription for gravitational charges in the presence of anomalies and field-dependent diffeomorphism, depending on a specific correlation between these factors. The mathematical interpretation of the allowed anomalies is revealed through the analysis of BMS symmetries, where they correspond to soft terms in the charges. We investigate the correspondence between the Wald-Zoupas prescription and an improved Noether charge, establishing a certain differential equation as a necessary condition, and finding that the resulting improved Noether charge's boundary Lagrangian usually contains a nontrivial corner term that can be determined in advance by a condition of anomaly freeness. Our findings shed light on the effectiveness of the Wald-Zoupas prescription despite the anomalous behavior of BMS transformations, and offer insights for connecting different aspects of surface charges literature.