Abstract
We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg 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. 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. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.
Highlights
The AdS/CFT correspondence [1,2,3,4,5,6,7] has revealed profound insights into the dualities equating theories with and without gravity
The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space
We derive the central objects of this conjectured 2D CFT — namely the conserved currents and stress tensor — and show how the corresponding Kac-Moody and Virasoro algebras beautifully encode the asymptotic symmetries of 4D gauge theory [20,21,22,23,24] and gravity [25,26,27]
Summary
The AdS/CFT correspondence [1,2,3,4,5,6,7] has revealed profound insights into the dualities equating theories with and without gravity. In our formulation, these memory effects are naturally encoded as abelian and non-abelian Aharonov-Bohm phases from the encircling of hard particle “tracks” by CS gauge fields. We define bulk and boundary coordinates natural to achieve this mapping
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