BRST cohomology ring in 2D gravity coupled to minimal models

Abstract

The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models coupled to gravity is shown to be $\mathcal{R}={\mathcal{R}}_0\otimes \mathbf{C}[w,w^{-1}]$ where ${\mathcal{R}}_0$ is the ring of ghost number zero operators generated by two elements and $w$ is an operator of ghost number $-1$. Some examples are discussed in detail. For these models the currents are also discussed and their algebra is shown to contain the Virasoro algebra.

19 pages IC/92/150