An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories

Abstract

We derive the soft effective action in $(d+2)$-dimensional abelian gauge theories from the on-shell action obeying Neumann boundary conditions at timelike and null infinity and Dirichlet boundary conditions at spatial infinity. This allows us to identify the on-shell degrees of freedom on the boundary with the soft modes living on the celestial sphere. Following the work of Donnelly and Wall, this suggests that we can interpret soft modes as entanglement edge modes on the celestial sphere and study entanglement properties of soft modes in abelian gauge theories.

25 pages, version appearing in PRD; v2: Corrected typos in Appendix A

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• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Modular Fluctuations in Cosmology
• Diamond of Infrared Equivalences in Abelian Gauge Theories
• From Asymptotically Flat Gravity to Finite Causal Diamonds
• Effective density matrix for vacua in asymptotically flat gravity