Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories

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.

39 pages, 3 figures, and 6 tables

References in corpus (6)

• 6d Conformal Matter
• Anomaly polynomial of general 6d SCFTs
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Small instanton transitions for M5 fractions

Cited by in corpus (2)

• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups