  We demonstrate a tree-level equivalence between four distinct infrared
objects in $(d+2)$-dimensional abelian gauge theories. These are ($i$) the
large gauge charge $Q_\varepsilon$ where the function $\varepsilon$ on the
sphere parameterizing large gauge transformations is identified with the
Goldstone mode $\theta$ of spontaneously broken large gauge symmetry; ($ii$)
the soft effective action that captures the dynamics of the soft and Goldstone
modes; ($iii$) the edge mode action with Neumann boundary conditions; and
($iv$) the Wilson line dressing of a scattering amplitude, including a novel
dressing for soft photons, which have local charge distributions despite having
vanishing global charge. The promotion of the large gauge parameter to the
dynamical Goldstone and the novel dressing of soft gauge particles give rise to
intriguing possibilities for the future study of infrared dynamics of gauge
theories and gravity.
