Magnetic Corrections to the Soft Photon Theorem

TL;DR

Strominger analyzes how the leading soft photon theorem is modified in the presence of magnetic monopoles and shows that duality fixes a magnetically corrected soft factor, conjectured to be exact for abelian theories. The work identifies an infinite tower of magnetic large gauge symmetries and demonstrates that electric and magnetic sectors form a complexified symmetry acting on the S-matrix, with soft photons as Goldstone modes. Furthermore, the magnetically corrected soft theorem is shown to be the Ward identity for these complexified large gauge transformations, implying infinite conserved charges for both electric and magnetic sectors. This provides a unified infrared structure for abelian gauge theories with monopoles and highlights the deep role of duality in asymptotic symmetries.

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.