Non-Geometric Vacua of the $\mathbf{\text{Spin}(32)/\mathbb Z_2}$ Heterotic String and Little String Theories

TL;DR

This paper investigates non-geometric vacua of the Spin(32)/Z2 heterotic string, analyzing their degenerations and dualities, and finds that many lead to little string theories or singularities without crepant resolutions.

Contribution

It systematically classifies degenerations of genus-two fibrations in heterotic vacua and explores their dual F-theory descriptions, revealing connections to little string theories and novel dualities.

Findings

Many dual threefolds contain unresolved singularities.

Resolved cases correspond to little string theories.

Identified dualities between theories on different defects.

Abstract

We study a class of 6d $\mathcal{N}=(1,0)$ non-geometric vacua of the $\text{Spin}(32)/\mathbb Z_2$ heterotic string which can be understood as fibrations of genus-two curves over a complex one-dimensional base. The 6d $\mathcal{N}=(1,0)$ theories living on the defects that arise when the genus-two fiber degenerates at a point of the base are analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We consider all possible degenerations of genus-two curves and systematically attempt to resolve the singularities of the dual threefolds. As in the analogous non-geometric vacua of the $E_8\times E_8$ heterotic string, we find that many of the resulting dual threefolds contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, we determine the emerging effective theories which turn out to be little string theories at a generic point on their tensor branch. We also observe a form of duality in which theories living on distinct defects are the same.