Abstract
Scattering amplitudes of any four-dimensional theory with nonabelian gauge group \( \mathcal{G} \) may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional \( \mathcal{G} \)-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.
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He, T., Mitra, P. & Strominger, A. 2D Kac-Moody symmetry of 4D Yang-Mills theory. J. High Energ. Phys. 2016, 137 (2016). https://doi.org/10.1007/JHEP10(2016)137
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DOI: https://doi.org/10.1007/JHEP10(2016)137