Charge algebra for non-abelian large gauge symmetries at $O(r)$

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.

Colored black holes and Kac-Moody algebra

“…In fact, it is possible to speculate that large gauge transformations could describe physical processes that produce a splash of colors on the horizon, for instance by means of a mechanism similar to the one studied in [12,16]. As in there, one can imagine dynamical processes that connect the asymptotic past null-infinity I − with the future horizon H + , using that now we have learnt that a similar Virasoro-Kac-Moody structure emerges in both regions [26,34,35].…”

“…All the arbitrary functions of z A can be expanded in Fourier modes, e.g. as usually done when representing Diff(S 1 ) or tensored C ∞ (S 1 ) algebras in conformal field theory: It amounts to choose complex coordinates z A = (z, z) with z = e τ +iσ , and evaluate ( 33)- (34) on arbitrary modes z m zn . That is to say, we can define…”