Embeddings and Integrable Charges for Extended Corner Symmetry

Abstract

We revisit the problem of extending the phase space of diffeomorphism-invariant theories to account for embeddings associated with the boundary of sub-regions. We do so by emphasizing the importance of a careful treatment of embeddings in all aspects of the covariant phase space formalism. In so doing we introduce a new notion of the extension of field space associated with the embeddings which has the important feature that the Noether charges associated with all extended corner symmetries are in fact integrable, but not necessarily conserved. We give an intuitive understanding of this description. We then show that the charges give a representation of the extended corner symmetry via the Poisson bracket, without central extension.

5 pages, published in PRL

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• Edge modes of gravity -- I: Corner potentials and charges
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Isolated Surfaces and Symmetries of Gravity
• Edge modes of gravity. Part III. Corner simplicity constraints
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Geometrical tools for embedding fields, submanifolds, and foliations

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