Exact Infrared Triangle in Massless sQED with Long-range Interactions

TL;DR

The authors analyze massless scalar QED with long-range electromagnetic interactions, constructing an asymptotic phase space that accounts for Coulombic and radiative effects at null infinity. They show that the divergent superphaserotation charge, which underpins the logarithmic soft photon theorem, vanishes to all orders in the electromagnetic coupling, and that the loop-corrected subleading charge and the logarithmic soft contributions likewise vanish, leaving no classical logarithmic infrared data. Consequently, the tail memory effect vanishes as well, so the full classical infrared triangle collapses to triviality in this massless setting. The results clarify the distinct infrared structure of massless matter coupled to long-range gauge fields and suggest future work to uncover a quantum symmetry interpretation of the surviving logarithmic soft photon sector.

Abstract

The logarithmic soft photon theorem in four spacetime dimensions encodes an infinite-dimensional asymptotic symmetry which acts on massive matter as a divergent superphaserotation. Here we extend this result to massless matter which is both more subtle and surprising. We derive the charge associated to divergent superphaserotations and show that it exactly vanishes to all orders in the electromagnetic coupling. This is in agreement with the vanishing of the classical logarithmic soft photon theorem which is one-loop exact. Special care is required for massless matter due to potential collinear divergences which, as we show, do however not affect the superphaserotation charge. We furthermore compute the infrared corrections to the charge associated to the subleading tree-level soft photon theorem. As a corollary of our result, we find that the tail to the velocity kick memory due to the long-range interactions between soft electromagnetic radiation and massless matter vanishes.