4D Flat Space Theory and Gravity in a 2D CFT

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT

We reformulate the scattering amplitudes of 4d flat space gauge theory and gravity in the language of a 2d cosmic field theory (cft) on the celestial sphere.Tree-level scattering amplitudes take the form of witten diagrams for a continuum of (a)ds modes, which are in turn equivalent to correlators via the (a)ds/cft dictionary.The ward identities for the 2dconserved currents are dual to 4d soft theorems, while the bulk-boundarypropagators of massless (a)ds modes are superpositions of the leading and subleading soft factors of gauge theory and gravity.In general, the massless (a)ds modes are 3d chern-simons gauge fields describing the soft, single helicity sectors of 4d gauge theory and gravity.We derive these results by recasting 4d dynamics in terms of a convenient foliation of flat space into a convenient foliation of flat space into 3d euclidean ads and 3d ds geometries.The resulting cftstructure exhibits an ope constructed from 4d collinear singularities, as well as infinite-dimensional kac-and virasoro algebras encoding the asymptotic symmetries of 4d flat space.Consistent with the topological nature of chern-simons theory, aharonov-bohm effects record the"tracks"of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories.