Abstract
Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.
Highlights
Decay as 1/r, it is useful in some circumstances to allow for “kinematical” components with slower fall-offs
In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity
This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, violate standard asymptotic field fall-offs and their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level
Summary
We consider pure classical Yang-Mills theory with a matrix group G in 4d flat spacetime. With ∇μ and Dμ denoting the metric and gauge covariant derivatives respectively. To describe the gauge field near future null infinity, we employ outgoing coordinates (r, u, xa), where r is the radial coordinate, u = t − r the retarded time, and xa coordinates on the celestial sphere. Points at null infinity I will be labeled as (u, x), with x = xa denoting a point on the celestial sphere. The gauge field near null infinity can be determined in terms of Aa(u, x) by solving the field equations We denote by Γrad the resulting space of gauge fields and write schematically. We denote by Da the gauge-covariant derivative at null infinity, Da := ∂a + [Aa, ],. Use ∂a to denote the sphere-covariant derivative compatible with qab, i.e.
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