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.

arXiv comment39 pages, 3 figures, and 6 tables

References in corpus (35)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Small Instantons in String Theory
• Vector Bundles And F Theory
• A Note on the Green - Schwarz Mechanism in Open - String Theories
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Geometric Constructions of Nongeometric String Theories
• Branes and Six Dimensional Supersymmetric Theories
• Anomaly polynomial of general 6d SCFTs
• New Phases of String Theory and 6d RG Fixed Points via Branes at Orbifold Singularities
• Point-like Instantons on K3 Orbifolds
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• The SO(32) Heterotic String on a K3 Surface
• Toric bases for 6D F-theory models
• RG Fixed Points in Six Dimensions via Branes at Orbifold Singularities
• Branes and Six Dimensional Fixed Points
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Point-like Instantons and the Spin(32)/Z2 Heterotic String
• 6D RG Flows and Nilpotent Hierarchies
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• On the Duality between the Heterotic String and F-Theory in 8 Dimensions
• T-branes, Anomalies and Moduli Spaces in 6D SCFTs
• Small instanton transitions for M5 fractions
• F-theory, SO(32) and Toric Geometry
• The Satake sextic in elliptic fibrations on K3
• Heterotic T-fects, 6D SCFTs, and F-Theory
• F-theory and Unpaired Tensors in 6D SCFTs and LSTs
• Mirror Symmetry via Deformation of Bundles on K3 Surfaces
• Ubiquity of non-geometry in heterotic compactifications
• The monodromy of T-folds and T-fects

Cited by in corpus (5)

• Revisiting the classifications of 6d SCFTs and LSTs
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• A note on T-folds and T3 fibrations
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups