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Heterotic T-fects, 6D SCFTs, and F-Theory

Anamaría Font, Iñaki García-Etxebarria, Dieter Lust, Stefano Massai, Christoph Mayrhofer

TL;DR

The paper develops a genus-two, heterotic/F-theory–driven framework to analyze non-geometric heterotic vacua (T-fects) preserving $E_8\times E_7$, dual to F-theory on elliptic K3-fibered Calabi–Yau threefolds. By classifying genus-two degenerations via the NU/OGG scheme and mapping to dual K3 geometries, it derives the 6D $(1,0)$ SCFT data on defects, including IR fixed points on tensor branches and their gauge/matter content; many non-geometric cases resolve to well-known ADE-instanton theories, while others realize genuinely new T-fect classes. A global construction shows how local degenerations assemble into CY3s and reveals a duality web in which distinct defects yield identical IR theories, offering tests for T-duality–covariant formalisms. Collectively, the work provides a comprehensive catalog of T-fects and their 6D SCFT realizations, bridging non-geometric heterotic vacua with familiar geometric instanton physics and outlining avenues for extending to four dimensions and broader duality frameworks.

Abstract

We study the $(1,0)$ six-dimensional SCFTs living on defects of non-geometric heterotic backgrounds (T-fects) preserving a $E_7\times E_8$ subgroup of $E_8\times E_8$. These configurations can be dualized explicitly to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We find that the majority of the resulting dual threefolds contain non-resolvable singularities. In those cases in which we can resolve the singularities we explicitly determine the SCFTs living on the defect. We find a form of duality in which distinct defects are described by the same IR fixed point. For instance, we find that a subclass of non-geometric defects are described by the SCFT arising from small heterotic instantons on ADE singularities.

Heterotic T-fects, 6D SCFTs, and F-Theory

TL;DR

The paper develops a genus-two, heterotic/F-theory–driven framework to analyze non-geometric heterotic vacua (T-fects) preserving , dual to F-theory on elliptic K3-fibered Calabi–Yau threefolds. By classifying genus-two degenerations via the NU/OGG scheme and mapping to dual K3 geometries, it derives the 6D SCFT data on defects, including IR fixed points on tensor branches and their gauge/matter content; many non-geometric cases resolve to well-known ADE-instanton theories, while others realize genuinely new T-fect classes. A global construction shows how local degenerations assemble into CY3s and reveals a duality web in which distinct defects yield identical IR theories, offering tests for T-duality–covariant formalisms. Collectively, the work provides a comprehensive catalog of T-fects and their 6D SCFT realizations, bridging non-geometric heterotic vacua with familiar geometric instanton physics and outlining avenues for extending to four dimensions and broader duality frameworks.

Abstract

We study the six-dimensional SCFTs living on defects of non-geometric heterotic backgrounds (T-fects) preserving a subgroup of . These configurations can be dualized explicitly to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. We find that the majority of the resulting dual threefolds contain non-resolvable singularities. In those cases in which we can resolve the singularities we explicitly determine the SCFTs living on the defect. We find a form of duality in which distinct defects are described by the same IR fixed point. For instance, we find that a subclass of non-geometric defects are described by the SCFT arising from small heterotic instantons on ADE singularities.

Paper Structure

This paper contains 34 sections, 180 equations, 6 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Non-geometric heterotic vacua
  3. Heterotic/F-theory duality in 8 dimensions
  4. From 8 to 6 dimensions: local models and exotic defects
  5. From 8 to 6 dimensions: global models.
  6. Geometric models: five-branes on ADE singularities
  7. $\mathrm{[I_0-II^{\ast}]}$ model and $E_8$ singularity
  8. Adding five-branes
  9. Five-branes on $\mathbb{C}^2/\mathbb{Z}_k$
  10. $[\mathrm{I}_{n-p-0}]$ model
  11. $[\mathrm{I}_{n-p-q}]$ model
  12. Non-geometric models and duality web
  13. Double elliptic T-fold: $\mathrm{[III-III]}$ model
  14. A global model
  15. Dualities
  16. ...and 19 more sections

Figures (6)

  • Figure 1: (a) The Humphries generators for a genus-two surface $\Sigma$: any element of the mapping class group $\mathcal{M}(\Sigma)$ can be written as a product of Dehn twists along the cycles $(a_1,b_1,\gamma,a_2,b_2)$. Note that $\gamma = a_1^{-1}a_2$. (b) Switching off the Wilson line parameter $\beta$ corresponds to splitting $\Sigma$ into two genus-one components. This geometrizes the $SL(2,\mathbb{Z})_{\tau}\times SL(2,\mathbb{Z})_{\rho}$ subgroup of the T-duality group $O(2,2,\mathbb{Z})$.
  • Figure 2: Resolution of the dual $\mathrm{[II^{\ast}-I_0]}$ model.
  • Figure 3: The NS5-D6-D8 configuration corresponding to the $\mathrm{[I_{5-3}]}$ model: circles with a cross represent NS5 branes, the horizontal lines are the D6's and the vertical line are D8 branes.
  • Figure 4: The NS5-D6-D8 configuration corresponding to the $[\mathrm{I}_{8-6-4}]$ model. We now have an additional D8 on the right hand side, which causes additional jumps in the rank of gauge groups.
  • Figure 5: Pictorial summary of the gauge algebra and matter content that arise from the resolution of the dual model of a $\mathrm{[III-III]}$ singularity.
  • ...and 1 more figures