On Physical States in c<1 String Theory

TL;DR

This paper explores the structure of physical states in c<1 string theory, revealing their relationships through descent equations and how ring elements facilitate calculating sphere correlation functions.

Contribution

It demonstrates the connection between states at different ghost numbers via descent equations derived from double cohomology, advancing understanding of physical states in c<1 string theory.

Findings

Physical states at all ghost numbers are related through descent equations.

Ring elements enable determination of all sphere correlation functions.

The analysis clarifies the structure of BRST cohomology in c<1 string theory.

Abstract

The BRST cohomology analysis of Lian and Zuckerman leads to physical states at all ghost number for $c<1$ matter coupled to Liouville gravity. We show how these states are related to states at ghost numbers zero(pure vertex operator states -- DK states) and ghost number one(ring elements) by means of descent equations. These descent equations follow from the double cohomology of the String BRST and Felder BRST operators. We briefly discuss how the ring elements allow one to determine all correlation functions on the sphere.