Diamond of infrared equivalences in abelian gauge theories

We demonstrate a tree-level equivalence between four distinct infrared objects in (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>2</a:mn></a:mrow></a:math>)-dimensional Abelian gauge theories. These are (i) the large gauge charge <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>Q</c:mi><c:mi>ϵ</c:mi></c:msub></c:math> where the function <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ϵ</e:mi></e:math> on the sphere parametrizing large gauge transformations is identified with the Goldstone mode <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>θ</g:mi></g:math> 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