Punctures in W-string theory

Using the differential equation approach to W-algebras, we discuss the inclusion of punctures in W-string theory. The key result is the existence of different kinds of punctures in W-strings. This is similar to the NS and R punctures occuring in superstring theories. We obtain the moduli associated with these punctures and present evidence in existing W-string theories for these punctures. The $W_3$ case is worked out in detail. It is conjectured that the $(1,3)$ minimal model coupled to two dimensional gravity corresponds to topological $W_3$-gravity.