Celestial Current Algebra from Low's Subleading Soft Theorem

TL;DR

The paper extends celestial holography by showing that Low's subleading soft photon theorem induces a second celestial current algebra, realized by the subleading boundary value A_{ar{z}}^{(1)}. This current acts on celestial operators with a nonstandard weight shift of 1/2 in each conformal dimension, reflecting the continuous principal-series nature of the representations involved. By recasting the subleading theorem as a celestial Ward identity, the work connects infrared structure of scattering to a new 2D symmetry on the celestial sphere, under simplifying assumptions that exclude long-range magnetic fields and massless scalar charges. Together, these results establish a framework for exploring subleading-gauge symmetries and their constraints on scattering amplitudes within celestial CFT.

Abstract

The leading soft photon theorem implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) $U(1)$ Kac-Moody symmetry that acts on the celestial sphere at null infinity ($\mathcal{I}$). This celestial $U(1)$ current is realized by components of the electromagnetic vector potential on the boundaries of $\mathcal{I}$. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of $\mathcal{I}$. The subleading soft photon theorem is reexpressed as a celestial Ward identity for this second current, which involves novel shifts by one unit in the conformal dimension of charged operators.