  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.
