Spectrum Generating Algebra and No-Ghost Theorem for Fermionic Massive String

TL;DR

This paper develops a spectrum generating algebra and proves a no-ghost theorem for a modified fermionic string model with supersymmetric Liouville sector, identifying tachyon-free theories in various dimensions.

Contribution

It constructs the spectrum generating algebra and establishes a general no-ghost theorem for a class of fermionic strings with supersymmetric modifications.

Findings

Constructed the spectrum generating algebra for the model.

Proved a general no-ghost theorem ensuring unitarity.

Identified a family of tachyon-free, unitary string theories.

Abstract

The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions $d=2,4,6,8$. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. A counterpart of the GSO projection leads to a family of tachyon free unitary free string theories. One of these models is equivalent to the non-critical Rammond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon free eigenspace of the fermion parity operator.