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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 transformations, and should be helpful to relate different branches of the literature on surface charges.
Odak et al. (Mon,) studied this question.
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