Magnetic Corrections to the Soft Photon Theorem

TL;DR

This paper extends the soft photon theorem to include magnetic charges, revealing new magnetic symmetries and conserved charges, and unifies electric and magnetic symmetries through complexification.

Contribution

It introduces magnetic corrections to the soft photon theorem and identifies associated magnetic gauge symmetries, expanding the understanding of asymptotic symmetries in abelian gauge theories.

Findings

Magnetic corrections lead to a second set of conserved charges.

Large magnetic gauge transformations are identified as symmetries.

Electric and magnetic symmetries are unified via complexification.

Abstract

The soft photon theorem, in its standard form, requires corrections when the asymptotic particle states carry magnetic charges. These corrections are deduced using electromagnetic duality and the resulting soft formula conjectured to be exact for all abelian gauge theories. Recent work has shown that the standard soft theorem implies an infinity of conserved electric charges. The associated symmetries are identified as `large' electric gauge transformations. Here the magnetic corrections to the soft theorem are shown to imply a second infinity of conserved magnetic charges. The associated symmetries are identified as `large' magnetic gauge transformations. The large magnetic symmetries are naturally subsumed in a complexification of the electric ones.