Extended corner symmetry, charge bracket and Einstein’s equations

• Published in: The journal of high energy physics Vol. 2021; no. 9; pp. 1 - 38
• Main Authors: Freidel, Laurent, Oliveri, Roberto, Pranzetti, Daniele, Speziale, Simone
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 15.09.2021; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Anomalies; Brackets; Classical and Quantum Gravitation; Classical Theories of Gravity; Elementary Particles; Equations of motion; Fields (mathematics); General Relativity and Quantum Cosmology; High energy physics; High Energy Physics - Theory; Mathematical analysis; Mathematical Physics; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Representations; Space-Time Symmetries; String Theory; Symmetry; Classical Theories of Gravity; Models of Quantum Gravity; Space-Time Symmetries; anomaly; surface; symmetry: algebra; phase space: covariance; field equations: gravitation; holography; flux; symmetry: translation; field theory: vector; Einstein equation
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP09(2021)083

A bstract We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies, and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.