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

Understand

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.