Note on asymptotic symmetries and soft gluon theorems

Recently, the leading soft gluon theorem with single soft emission was shown to be the Ward identity of a two dimensional $\mathcal{G}$-Kac-Moody symmetry. In this note, we show that the leading soft gluon theorem can be interpreted as the Ward identity for the asymptotic symmetries of non-Abelian gauge theory. We further argue that the sub-leading soft gluon theorem can follow from the same symmetry.