Diamond of Infrared Equivalences in Abelian Gauge Theories

TL;DR

This paper establishes a tree-level equivalence among four infrared objects in abelian gauge theories, linking large gauge charges, soft modes, edge modes, and Wilson line dressings, with implications for infrared dynamics.

Contribution

It introduces a novel equivalence connecting large gauge charges, soft effective actions, edge modes, and Wilson line dressings in abelian gauge theories.

Findings

Identifies the large gauge charge with the Goldstone mode.

Derives a soft effective action for soft and Goldstone modes.

Proposes a new dressing for soft photons with local charge distributions.

Abstract

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.