The Weyl BMS group and Einstein’s equations
Laurent Freidel (Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada); Roberto Oliveri (CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, Praha 8, 182 21, Czech Republic); Daniele Pranzetti (Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada, Università degli Studi di Udine, via Palladio 8, Udine, I-33100, Italy); Simone Speziale (CPT-UMR 7332, CNRS, Marseille, 13288, France)
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.
