# Celestial Current Algebra from Low's Subleading Soft Theorem

## TL;DR

This paper extends the celestial symmetry framework by deriving a second current from Low's subleading soft photon theorem, revealing new Ward identities involving shifts in conformal dimensions of charged operators.

## Contribution

It introduces a new celestial current associated with the subleading soft photon theorem and formulates its Ward identity, expanding the celestial symmetry structure.

## Key findings

- Identifies a second celestial $U(1)$ current from subleading soft photons.
- Reexpresses the subleading soft theorem as a celestial Ward identity.
- Shows shifts in conformal dimension of charged operators.

## 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.