  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.
