Coadjoint representation of the BMS group on celestial Riemann surfaces

127

161

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.

Section: Vacuum Structurementioning

confidence: 99%

The Weyl BMS group and Einstein’s equations

Freidel

Oliveri

Pranzetti

et al. 2021

127

161

“…In [18], the coadjoint representation of the BMS group in four dimensions has been constructed. It acts on a set of conformal fields that have been identified with local expressions of the solution space of non-radiative asymptotically flat spacetimes at null infinity JHEP11(2021)040 through a (pre-)momentum map.…”

Section: Introductionmentioning

confidence: 99%

BMS flux algebra in celestial holography

Donnay

Ruzziconi

2021

Self Cite

Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

“…In terms of it, we examined physically relevant non-central extensions and came up with some simple free field realizations. Remarkably, the two-punctured Riemann sphere, where the conformal subalgebra of (3.2) and of (3.6) is consistently realized, has been argued to be the relevant one for celestial scattering amplitudes and soft theorems in the context of bms [37,[54][55][56]. Analogously, we expect the complete (3.2) and (3.6) to play the equivalent role for gbms.…”

Section: Jhep10(2021)133 4 Summary and Conclusionmentioning

confidence: 66%

On deformations and extensions of Diff(S2)

Rojo

Procházka

Sachs

2021

We investigate the algebra of vector fields on the sphere. First, we find that linear deformations of this algebra are obstructed under reasonable conditions. In particular, we show that hs[λ], the one-parameter deformation of the algebra of area-preserving vector fields, does not extend to the entire algebra. Next, we study some non-central extensions through the embedding of $$ \mathfrak{vect} $$ vect (S2) into $$ \mathfrak{vect} $$ vect (ℂ*). For the latter, we discuss a three parameter family of non-central extensions which contains the symmetry algebra of asymptotically flat and asymptotically Friedmann spacetimes at future null infinity, admitting a simple free field realization.