Fractional Superstrings with Space-Time Critical Dimensions Four and Six

TL;DR

This paper introduces new string theories with fractional superconformal symmetries, featuring unique critical dimensions and space-time supersymmetry, supported by modular invariance and particle spectrum analysis.

Contribution

It proposes novel fractional superstring models with specific critical dimensions and demonstrates their consistency through modular invariance and spectral properties.

Findings

Existence of string theories with critical dimensions 4 and 6.

Construction of modular invariant partition functions.

Presence of space-time supersymmetry in these models.

Abstract

We propose possible new string theories based on local world-sheet symmetries corresponding to extensions of the Virasoro algebra by fractional spin currents. They have critical central charges $c=6(K+8)/(K+2)$ and Minkowski space-time dimensions $D=2+16/K$ for $K\geq2$ an integer. We present evidence for their existence by constructing modular invariant partition functions and the massless particle spectra. The dimension $4$ and $6$ strings have space-time supersymmetry.