The Complete Cohomology of the W3 String
H. Lu, C.N. Pope, X.J. Wang, K.W. Xu

TL;DR
This paper introduces a straightforward method to determine the complete cohomology of the BRST operator in W3 string theories, using invertible physical operators to classify all physical states.
Contribution
It provides a novel, simplified procedure for constructing the full cohomology of the BRST operator in W3 string models, enabling exhaustive classification of physical operators.
Findings
Constructed two level-15 physical operators that are invertible.
Mapped all physical operators into a fundamental unit cell.
Solved the entire cohomology problem for the W3 string.
Abstract
We present a simple procedure for constructing the complete cohomology of the BRST operator of the two-scalar and multi-scalar strings. The method consists of obtaining two level--15 physical operators in the two-scalar string that are invertible, and that can normal order with all other physical operators. They can be used to map all physical operators into non-trivial physical operators whose momenta lie in a fundamental unit cell. By carrying out an exhaustive analysis of physical operators in this cell, the entire cohomology problem is solved.
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