New Magnetic Symmetries in $(d+2)$-Dimensional QED

TL;DR

The paper shows that in $(d{+}2)$-dimensional QED the subleading soft photon theorem is equivalent to a set of Ward identities arising from a family of angular matching conditions at null infinity. The charges decompose into soft and hard pieces, with the soft sector yielding an electric-type Ward identity and a novel magnetic-type Ward identity from angular magnetic data; the authors prove both directions of equivalence between the subleading theorem and these Ward identities. They analyze the asymptotic fields, derive the necessary matching conditions, and compute hard-charge actions on multi-particle states, demonstrating how electric and magnetic large gauge transformations act in the $S$-matrix. This leads to the existence of a finite magnetic asymptotic symmetry in QED, even in the absence of global magnetic charges, thereby enriching the structure of asymptotic symmetries in gauge theories across dimensions.

Abstract

Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity. In this work, we demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity. The charge corresponding to this Ward identity can be decomposed into an electric piece and a magnetic piece. The electric piece generates the Ward identity that was previously studied, but the magnetic piece is novel, and implies the existence of an additional asymptotic "magnetic" symmetry in QED.