Strings on Eight-Orbifolds

TL;DR

This work constructs and analyzes $T^8/P$ orbifolds with $P\subset SU(4)$, computing their Hodge numbers and exploring discrete torsion. Using SCFT, the authors connect orbifold spectra to CY$_4$-like geometry, and examine supersymmetric compactifications of Type II, heterotic, and Type I strings in $D=2$, detailing anomaly cancellation and tadpole conditions. A central result is that heterotic tadpoles, derived from the $B$-field coupling $\int B\wedge X_8$, can be canceled either by a precise Euler number in standard embeddings or by non-standard embeddings, sometimes aligning with Type I orientifold constructions; explicit tadpole-free examples are exhibited. The study reveals a network of perturbative and non-perturbative mechanisms to realize consistent $D=2$ vacua across string theories, and points to further investigations in dualities and higher-dimensional uplifts (M-/F-theory). Overall, the paper provides a framework for systematic construction and analysis of eight-dimensional orbifold compactifications and their low-dimensional effective 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.