Asymptotic Symmetries of Massless QED in Even Dimensions

TL;DR

The paper extends the known link between soft photon theorems and asymptotic symmetries from four to all even dimensions by showing that Weinberg's leading soft factor for massless QED can be recast as a Ward identity for a new class of large, angle-dependent U(1) gauge transformations at null infinity. It provides a concrete six-dimensional analysis with explicit boundary data, zero-mode operators, and matching conditions, demonstrating that soft charges act as Goldstone modes and that hard charges implement gauge transformations on matter, thereby revealing an extended asymptotic symmetry structure. The results generalize to arbitrary even dimensions, outlining the necessary phase-space, operator relations, and boundary conditions, and highlighting the universal infrared structure of gauge theories across dimensions.

Abstract

We consider the scattering of massless particles coupled to an abelian gauge field in 2n-dimensional Minkowski spacetime. Weinberg's soft photon theorem is recast as Ward identities for infinitely many new nontrivial symmetries of the massless QED S-matrix, with one such identity arising for each propagation direction of the soft photon. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters that are constant along the null generators of null infinity. Almost all of the symmetries are spontaneously broken in the standard vacuum and the soft photons are the corresponding Goldstone bosons. Our result establishes a relationship between soft theorems and asymptotic symmetry groups in any even dimension.