The Weyl BMS group and Einstein’s equations

• Published in: The journal of high energy physics Vol. 2021; no. 7; pp. 1 - 65
• Main Authors: Freidel, Laurent, Oliveri, Roberto, Pranzetti, Daniele, Speziale, Simone
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Algebra; Classical and Quantum Gravitation; Classical Theories of Gravity; Elementary Particles; General Relativity and Quantum Cosmology; Gravity; High energy physics; High Energy Physics - Theory; Infinity; Isomorphism; Lie groups; Mathematical analysis; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; String Theory; Symmetry; Translations; Classical Theories of Gravity; Models of Quantum Gravity; Space-Time Symmetries; algebra: Lie; rescaling; phase space; symplectic; charge: Noether; renormalization: holography; group: Weyl; Einstein equation; diffeomorphism
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP07(2021)170

A bstract We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein’s equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.