4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT

TL;DR

This paper reformulates 4D flat space gauge and gravity scattering amplitudes as a 2D CFT on the celestial sphere, revealing deep connections between asymptotic symmetries, soft theorems, and holographic dualities.

Contribution

It introduces a novel 2D CFT framework for 4D scattering amplitudes, linking asymptotic symmetries to CFT structures and soft theorems through a geometric and holographic approach.

Findings

CFT structure encodes 4D collinear singularities and asymptotic symmetries.

Soft theorems correspond to Ward identities of 2D conserved currents.

Gauge and gravitational memories are characterized by Aharonov-Bohm effects in the CFT.

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.