Non-BPS Fractional Branes with Bose-Fermi Cancellation in Asymmetric Orbifolds

TL;DR

This paper investigates non-BPS fractional D-branes in asymmetric orbifolds of K3, revealing conditions under which their self-overlaps vanish due to discrete torsion, contrasting with bulk branes.

Contribution

It demonstrates how discrete torsion can induce bose-fermi cancellations in fractional branes, extending understanding of non-BPS brane spectra in asymmetric orbifold models.

Findings

Cylinder partition functions for fractional branes do not vanish without discrete torsion.

Certain discrete torsion choices lead to vanishing self-overlaps, indicating bose-fermi cancellation.

The model maintains a vanishing torus partition function despite the presence of fractional branes.

Abstract

We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of $\mbox{K3} \cong T^4/{\Bbb Z}_2$ as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss the extensions of models by including the discrete torsion depending on the spin structures, and investigate whether we obtain the vanishing self-overlaps associated to the fractional branes. The existence/absence of bose-fermi cancellations both in the closed and open string spectra as well as the massless spectra in the twisted sectors crucially depend on the discrete torsion. We find that some choices of the torsion indeed realize the vanishing self-overlaps for the fractional branes, with keeping the vanishing torus partition function intact.