Diamond of infrared equivalences in abelian gauge theories

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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 ϵ where the function ϵ on the sphere parametrizing large gauge transformations is identified with the Goldstone mode θ 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. Published by the American Physical Society 2024
Funding Information
  • Heising-Simons Foundation (2021-2817)
  • U.S. Department of Energy (DE-SC0011632)
  • Walter Burke Institute for Theoretical Physics
  • H2020 European Research Council
  • Horizon 2020 Framework Programme (852386)

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