Loop Corrected Soft Photon Theorem as a Ward Identity

Abstract

Recently Sahoo and Sen obtained a series of remarkable results concerning sub-leading soft photon and graviton theorems in four dimensions. Even though the S- matrix is infrared divergent, they have shown that the sub-leading soft theorems are well defined and exact statements in QED and perturbative Quantum Gravity. However unlike the well studied Cachazo-Strominger soft theorems in tree-level amplitudes, the new sub-leading soft expansion is at the order ln ω (where ω is the soft frequency) and the corresponding soft factors structurally show completely different properties then their tree-level counterparts. Whence it is natural to ask if these theorems are associated to asymptotic symmetries of the S-matrix. We consider this question in the context of sub-leading soft photon theorem in scalar QED and show that there are indeed an infinity of conservation laws whose Ward identities are equivalent to the loop-corrected soft photon theorem. This shows that in the case of four dimensional QED, the leading and sub-leading soft photon theorems are equivalent to Ward identities of (asymptotic) charges.

33 pages, no figures

References in corpus (5)

• Low's Subleading Soft Theorem as a Symmetry of QED
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Null infinity, the BMS group and infrared issues
• Asymptotic charges in massless QED revisited: A view from Spatial Infinity

Cited by in corpus (25)

• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• Goldilocks Modes and the Three Scattering Bases
• Classical Soft Graviton Theorem Rewritten
• Conformal properties of soft operators -- 2 : Use of null-states
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• New Asymptotic Conservation laws for Electromagnetism
• Soft Photon theorem in the small negative cosmological constant limit
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit
• Soft factors from classical scattering on the Reissner-Nordström spacetime
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• Dressed-Asymptotic States and QED Infrared Physics
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Electromagnetic multipole expansions and the logarithmic soft photon theorem
• Asymptotic conservation law with Feynman boundary condition
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Scalar subleading soft theorems from an infinite tower of charges
• Flat Holography & Holographic Renormalization: Scalar Field
• Perturbative soft graviton theorems in de Sitter spacetime
• de Sitter corrections to supertranslation Ward identity and soft graviton theorem
• Subleading soft radiation during scattering of dressed states in QED
• Anomaly Equation of the Large U(1) Chiral Symmetry