Kac-Moody symmetry in the light front of gauge theories

Hernán A. González, Oriana Labrin, Olivera Miskovic

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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 U(1) current algebra with a level proportional to the coupling constant of the theory, κ = 4π 2/e 2. 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.

Original languageEnglish
Article number165
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jul 2023


  • Gauge Symmetry
  • Global Symmetries
  • Scale and Conformal Symmetries
  • Space-Time Symmetries


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