Abstract
Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev-Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff( {mathcal{S}}^2 ) superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern-Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.
Highlights
Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev-Shatashvili action on the celestial sphere
This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff(S2) superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern-Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere
Imposing the standard Newman-Unti boundary conditions at future null infinity I + [24], we show that the set of residual large gauge symmetries generates the extended/generalized bms4 algebra together with boundary Weyl rescalings, in agreement with an earlier analysis performed by Barnich and Lambert [25]
Summary
We start by describing the Newman-Unti gauge and associated boundary conditions, both in metric and first order formulation. We discuss residual asymptotic symmetries, recovering the extended/generalized BMS4 symmetries together with boundary Weyl rescalings [25]
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