Universality of soft theorem from locality of soft vertex operators

The universal behavior of the soft theorem at the tree level is explained by considering the operator product expansion of the soft and hard vertex operators. We find that the world-sheet integral for the soft vertex is determined only by the regions that are close to the hard vertices after eliminating total derivative terms. This analyses can be applied to massless particles in various theories such as bosonic closed string, closed superstring and heterotic string.