Wald-Zoupas prescription with (soft) anomalies

TL;DR

This paper demonstrates that the Wald-Zoupas prescription for gravitational charges remains valid with anomalies and field-dependent diffeomorphisms if they are related in a specific way, clarifying its applicability in BMS symmetries.

Contribution

It establishes conditions under which the Wald-Zoupas prescription is consistent with anomalies, providing a geometric interpretation and linking it to improved Noether charges.

Findings

Wald-Zoupas prescription is valid with certain anomalies

Conditions for equivalence with improved Noether charges are derived

Boundary Lagrangian contains corner terms related to anomaly-freeness

Abstract

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 non-trivial 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 behaviour of BMS transformations, and should be helpful to relate different branches of the literature on surface charges.