New Symmetries of Massless QED

TL;DR

This work demonstrates that massless QED possesses infinite-dimensional asymptotic U(1) symmetries generated by large gauge transformations approaching angle-dependent functions on the conformal sphere at I^+. By augmenting the radiative phase space with boundary soft modes and enforcing antipodal matching with I^-, the authors construct canonical charges whose Ward identity reproduces the soft photon theorem. Non-constant large gauge transformations are shown to be spontaneously broken, with zero-momentum photons acting as Goldstone modes on the sphere at infinity, and a diagonal symmetry identified across I^+ and I^- preserves the S-matrix. The results unify infrared aspects of gauge theories with asymptotic symmetries, offering a framework with potential implications for precision predictions and holographic considerations.

Abstract

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large $U(1)$ gauge transformations that asymptotically approach an arbitrary function $\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity ($\mathscr I^+$) but are independent of the retarded time. The value of $\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on $\mathscr I^+$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\varepsilon\neq$ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a $U(1)$ boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.