The effective action of superrotation modes

Abstract

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( S 2 $$ {\mathcal{S}}^2 $$ ) 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.

Keywords

• Classical Theories of Gravity
• Space-Time Symmetries
• Chern-Simons Theories
• Spontaneous Symmetry Breaking