Wald-Zoupas prescription with (soft) anomalies

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.

19 pages plus Appendix. V2: many improvements to the text, clarifications added, improved comparison with the results in the literature. More general analysis of the WZ covariance requirement, leading to a simpler discussion of some results at future null infinity. V3: minor amendments, matches published version

References in corpus (10)

• Asymptotic symmetries and subleading soft graviton theorem
• Setting the boundary free in AdS/CFT
• Surface charge algebra in gauge theories and thermodynamic integrability
• Null boundary phase space: slicings, news and memory
• The Precession Caused by Gravitational Waves
• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
• Charges and Fluxes on (Perturbed) Non-expanding Horizons
• Metric reconstruction from celestial multipoles
• Gravitational dynamics: A novel shift in the Hamiltonian paradigm
• Metriplectic geometry for gravitational subsystems

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• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
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• Mechanics as a general-relativistic gauge field theory, and Relational Quantization