The effective action of superrotation modes
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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($$ {\mathcal{S}}^2 $$ 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.
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1991 ◽
Vol 06
(06)
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pp. 479-486
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1999 ◽
Vol 09
(PR10)
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pp. Pr10-223-Pr10-225
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