Non-geometric heterotic backgrounds and 6D SCFTs/LSTs

TL;DR

This paper explores six-dimensional theories on defects in non-geometric heterotic string backgrounds, using F-theory duality to analyze singularities and reveal dualities among defect theories, including those from small heterotic instantons on ADE singularities.

Contribution

It provides a detailed analysis of non-geometric heterotic backgrounds and their dual F-theory descriptions, identifying new dualities and classifying defect theories such as SCFTs and LSTs.

Findings

Most dual threefolds contain unresolved singularities.

Resolved singularities lead to explicit defect theories.

Identifies dualities where different defects share the same IR fixed point.

Abstract

We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of non-geometric backgrounds of the $E_8\times E_8$ and the $\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. The majority of the resulting dual threefolds turn out to contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, the theories living on the defect are explicitly determined and reveal a form of duality in which distinct defects are described by the same IR fixed point. In particular, a subclass of non-geometric defects corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE singularities.