Extra States in C<1 String Theory

TL;DR

This paper constructs and analyzes extra states in c<1 string theory, clarifying their relation to null vectors and computing their two-point functions, thereby advancing understanding of the BRS cohomology structure.

Contribution

It provides a detailed construction of BRS cohomology elements with ghost number ±1 and relates these to null vectors in c<1 string theory, including explicit two-point function calculations.

Findings

Extra states are explicitly constructed in BRS cohomology.

The relation between these states and null vectors is clarified.

Two-point functions of these states are computed on the sphere.

Abstract

A construction of elements of the BRS cohomology of ghost number +/- 1 in c<1 string theory is described, and their two-point function computed on the sphere. The construction makes precise the relation between these extra states and null vectors. The physical states of ghost number +1 are found to be exact forms with respect to a ``conjugate'' BRS operator.