Strings on Eight-Orbifolds

TL;DR

This paper explores specific eight-dimensional orbifolds with SU(4) symmetry, analyzing their geometric properties and implications for supersymmetric string compactifications, including tadpole conditions and anomaly considerations.

Contribution

It provides new examples of T^8/P orbifolds, computes their Hodge numbers, and investigates their role in supersymmetric string compactifications with novel tadpole cancellation conditions.

Findings

Constructed orbifolds with specific Hodge numbers

Identified tadpole-free heterotic orbifolds with non-standard embedding

Analyzed anomaly and tadpole conditions in various string theories

Abstract

We present several examples of T^8/P orbifolds with $P \subset SU(4)$. We compute their Hodge numbers and consider turning on discrete torsion. We then study supersymmetric compactifications of type II, heterotic, and type I strings on these orbifolds. Heterotic compactifications to D=2 have a B-field tadpole with coefficient given by that of the anomaly polynomial. In the SO(32) heterotic with standard embedding the tadpole is absent provided the internal space has a precise value of the Euler number. Guided by their relation to type I, we find tadpole-free SO(32) heterotic orbifolds with non-standard embedding.