The Λ-BMS4 charge algebra

• Published in: The journal of high energy physics Vol. 2020; no. 10; pp. 1 - 45
• Main Authors: Compère, Geoffrey, Fiorucci, Adrien, Ruzziconi, Romain
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Asymptotic properties; Boundary conditions; Classical and Quantum Gravitation; Classical Theories of Gravity; Elementary Particles; Gauge Symmetry; High energy physics; Isomorphism; Lorentz transformations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; Spacetime; String Theory; Surface charge; Gauge Symmetry; Classical Theories of Gravity; Space-Time Symmetries
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2020)205

A bstract The surface charge algebra of generic asymptotically locally (A)dS 4 spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The Λ-BMS 4 charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS 4 charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS 4 surface charges represent the BMS 4 algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS 4 flux algebra admits no non-trivial central extension.