$W$ Strings and Cohomology in Parafermionic Theories

TL;DR

This paper establishes a connection between the cohomology in parafermionic theories and $W$ strings, offering a systematic approach to identify states in the cohomology of $W_{2,s}$ strings.

Contribution

It introduces a systematic method to find cohomology states in $W_{2,s}$ strings by relating them to parafermionic theories through locality constraints.

Findings

Cohomology in parafermionic theories is related to that in $W$ strings.

A systematic method for identifying states in $W_{2,s}$ string cohomology.

Provides new insights into the structure of $W$ string theories.

Abstract

By enforcing locality we relate the cohomology found in parafermionic theories to that occurring in $W$ strings. This link provides a systematic method of finding states in the cohomology of $W_{2,s}$ strings.