Aspects of Fractional Superstrings

TL;DR

This paper explores fractional superstring theories with less than 10 dimensions, rederives partition functions, examines supersymmetry, and clarifies the role of twist fields and anomaly relationships.

Contribution

It systematically rederives partition functions for specific models, finds generalized GSO projections, and clarifies the role of twist fields and anomaly relationships in fractional superstrings.

Findings

Partition functions for K=4, 8, 16 models are rederived.

Generalized GSO projection operators are identified for the K=4 model.

A linear relationship between conformal anomaly and supercurrent ghost dimension is established.

Abstract

We investigate some issues relating to recently proposed fractional superstring theories with $D_{\rm critical}<10$. Using the factorization approach of Gepner and Qiu, we systematically rederive the partition functions of the $K=4,\, 8,$ and $16$ theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the $K=4$ model are found. Uniqueness of the twist field, $\phi^{K/4}_{K/4}$, as source of spacetime fermions is demonstrated. Last, we derive a linear (rather than quadratic) relationship between the required conformal anomaly and the conformal dimension of the supercurrent ghost.