Kac-Moody symmetry in the light front of gauge theories

Hernán González (Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Diagonal Las Torres, Santiago, 2640, Chile) ; Oriana Labrin (Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avda. Universidad 330, Curauma, Valparaíso, Chile) ; Olivera Miskovic (Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avda. Universidad 330, Curauma, Valparaíso, Chile)

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.

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      "source": "Springer", 
      "value": "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, \u03ba = 4\u03c0 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."
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Published on:
26 June 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 6
Pages 1-28
DOI:
https://doi.org/10.1007/JHEP06(2023)165
arXiv:
2304.03211
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: