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 ( I ). This celestial U ( 1 ) current is realized by components of the electromagnetic vector potential on the boundaries of 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 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.
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