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Kac-Moody symmetry in the light front of gauge theories
We discuss the emergence of a new symmetry generator in a Hamiltonian
realisation of four-dimensional gauge theories in the flat space foliated by
retarded (advanced) time. It generates an asymptotic symmetry that acts on the
asymptotic fields in a way different from the usual large gauge
transformations. The improved canonical generators, corresponding to gauge and
asymptotic symmetries, form a classical Kac-Moody charge algebra with a
non-trivial central extension. In particular, we describe the case of
electromagnetism, where the charge algebra is the current
algebra with a level proportional to the coupling constant of the theory,
. We construct bilinear generators yielding Virasoro
algebras on the null boundary. We also provide a non-Abelian generalization of
the previous symmetries by analysing the evolution of Yang-Mills theory in
Bondi coordinates.Comment: 31 pages, no figures; in V2 text clarified and references adde