The infrared sector of gauge theory and gravity is plagued by divergences: scattering amplitudes involving massless particles emit infinite numbers of soft photons or gravitons, making the S-matrix formally infinite. Faddeev and Kulish showed in 1970 that “dressing” external states with clouds of soft radiation cures the divergence, but the dressing has always seemed like a technical fix rather than a structural principle.
Choi and Mitra construct a two-dimensional action on the celestial sphere — the sphere at null infinity where scattering data lives — that reproduces the entire infrared sector. The soft photon and graviton theorems, the antipodal matching conditions for Goldstone modes, and the infrared factorization of amplitudes all emerge from this 2D holographic action.
Within this framework, Faddeev-Kulish dressing is natural. The dressed states are the correct asymptotic states of the celestial theory — they arise from the boundary conditions, not from a prescription to cure divergences. Undressed states are infrared-divergent because they violate the boundary conditions. The divergence is a symptom of the wrong boundary data, not a fundamental problem with the theory.
The authors construct an infinite class of dressed states that yield infrared-finite scattering amplitudes, parameterized by different choices of soft radiation profile. The original Faddeev-Kulish dressing is one member of this class.
The soft sector of four-dimensional physics, reduced to a two-dimensional theory on a sphere. The infrared problem doesn't need to be solved — it needs to be reformulated in the geometry where it's already solved.