Punctures in W-string theory

TL;DR

This paper explores the inclusion of punctures in W-string theory using differential equations, identifying different puncture types and their moduli, with detailed analysis of the W3 case and conjectures relating to minimal models and topological gravity.

Contribution

It introduces the concept of various punctures in W-string theory and analyzes their moduli, extending the understanding of W-string structures and their relation to minimal models.

Findings

Existence of different puncture types in W-strings.

Moduli associated with these punctures are identified.

Evidence supports the presence of these punctures in existing W-string theories.

Abstract

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.