The Ring Structure of Chiral Operators for Minimal Models Coupled to 2D Gravity

TL;DR

This paper analyzes the algebraic structure of chiral operators in minimal models coupled to 2D gravity, revealing a new generator and its inverse that help construct the full BRST cohomology ring.

Contribution

It introduces a generator of ghost number -1 and its inverse, expanding the understanding of the BRST cohomology ring in minimal models coupled to gravity.

Findings

Existence of a ghost number -1 generator and its inverse.

Construction of the entire BRST cohomology ring.

Comments on algebraic structures and supersymmetric extensions.

Abstract

(Talk presented at the 1992 ICTP summer workshop in high energy physics and cosmology) The BRST cohomology ring for $(p,q)$ models coupled to gravity is discussed. In addition to the generators of the ghost number zero ring, the existence of a generator of ghost number $-1$ and its inverse is proven and used to construct the entire ring. Some comments are made regarding the algebra of the vector fields on the ring and the supersymmetric extension.