Diamond of Infrared Equivalences in Abelian Gauge Theories

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 $Q_{\epsilon }$ where the function $\epsilon$ 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.

8 pages, 1 figure; v2: Clarified discussion in Section III.C, minor clarification footnotes added, version to appear in PRD

References in corpus (13)

• Low's Subleading Soft Theorem as a Symmetry of QED
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Hard-Soft-Collinear Factorization to All Orders
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Spacetime Fluctuations in AdS/CFT
• Modular Fluctuations from Shockwave Geometries
• Non-abelian infrared divergences on the celestial sphere
• Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories
• Dynamical Edge Modes and Entanglement in Maxwell Theory
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• Entanglement, Soft Modes, and Celestial Holography
• An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories
• Asymptotic Structure of Higher Dimensional Yang-Mills Theory

Cited by in corpus (3)

• Modular Fluctuations in Cosmology
• From Asymptotically Flat Gravity to Finite Causal Diamonds
• Effective density matrix for vacua in asymptotically flat gravity