Multi-Soft gluon limits and extended current algebras at null-infinity

Abstract

In this note we consider aspects of the current algebra interpretation of multi-soft limits of tree-level gluon scattering amplitudes in four dimensions. Building on the relation between a positive helicity gluon soft-limit and the Ward identity for a level-zero Kac-Moody current, we use the double-soft limit to define the Sugawara energy-momentum tensor and, by using the triple- and quadruple-soft limits, show that it satisfies the correct OPEs for a CFT. We study the resulting Knizhnik-Zamolodchikov equations and show that they hold for positive helicity gluons in MHV amplitudes. Turning to the sub-leading soft-terms we define a one-parameter family of currents whose Ward identities correspond to the universal tree-level sub-leading soft-behaviour. We compute the algebra of these currents formed with the leading currents and amongst themselves. Finally, by parameterising the ambiguity in the double-soft limit for mixed helicities, we introduce a non-trivial OPE between the holomorphic and anti-holomorphic currents and study some of its implications.

24 pages, 1 figure

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Cited by in corpus (11)

• The Holographic Nature of Null Infinity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Subleading Power Factorization with Radiative Functions
• Descendants in celestial CFT and emergent multi-collinear factorization
• On Sugawara construction on Celestial Sphere
• Asymptotic Charges and Coherent States in QCD
• On the Symmetry Foundation of Double Soft Theorems
• Leading multi-soft limits from scattering equations
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Non-abelian soft radiation data for a celestial theory