Signature Characters for the Virasoro Algebra

TL;DR

This paper derives explicit formulas for signature characters of Virasoro algebra representations, completing prior analysis and aiding understanding of ghost states in non-unitary conformal field theories.

Contribution

It provides new expressions for signature characters of Virasoro algebra highest weight representations, extending Friedan-Qiu-Shenker's work.

Findings

Explicit formulas for signature characters derived.

Completes previous analysis of Virasoro representations.

Enhances understanding of ghost states in non-unitary theories.

Abstract

The number of ghost states at each energy level in a non-unitary conformal field theory is encoded in the signature characters of the relevant Virasoro algebra highest weight representations. We give expressions for these signature characters. These results complete Friedan-Qiu-Shenker's analysis of the Virasoro algebra's highest weight representations.