Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-Simply-Connected Symmetries in 6D SCFTs

Markus Dierigl, Paul-Konstantin Oehlmann, Fabian Ruehle

TL;DR

<3-5 sentence high-level summary>We classify 6d N=(1,0) SCFTs engineered via F-theory in the presence of Mordell-Weil torsion, which enforces a non-trivial global group structure by modding out center elements and restricting representations. The authors develop a torsion-aware framework for constructing tensor branches, starting from non-Higgsable clusters and SCMs, and analyze how these global constraints modify flavor and gauge groups, anomalies, and possible deformations. They connect these geometric realizations to heterotic and M-theory perspectives, interpreting torsion as discrete holonomy instantons and orbifold sectors, and they provide a comprehensive SCM zoo organized by torsion type with explicit tensor-branch data. The results offer a principled path to a global-classification of 6d SCFTs with non-simply-connected symmetries and have implications for compactifications and lower-dimensional duals.

Abstract

Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

Non-Simply-Connected Symmetries in 6D SCFTs

TL;DR

<3-5 sentence high-level summary>We classify 6d N=(1,0) SCFTs engineered via F-theory in the presence of Mordell-Weil torsion, which enforces a non-trivial global group structure by modding out center elements and restricting representations. The authors develop a torsion-aware framework for constructing tensor branches, starting from non-Higgsable clusters and SCMs, and analyze how these global constraints modify flavor and gauge groups, anomalies, and possible deformations. They connect these geometric realizations to heterotic and M-theory perspectives, interpreting torsion as discrete holonomy instantons and orbifold sectors, and they provide a comprehensive SCM zoo organized by torsion type with explicit tensor-branch data. The results offer a principled path to a global-classification of 6d SCFTs with non-simply-connected symmetries and have implications for compactifications and lower-dimensional duals.

Abstract

Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

Paper Structure

This paper contains 33 sections, 172 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Mordell-Weil Torsion and Restricted Monodromies
  3. F-Theory and Weierstrass Models
  4. Non-Simply-Connected Groups from Mordell-Weil Torsion
  5. 6d SCFTs
  6. 6d SCFTs and F-Theory
  7. The Heterotic Perspective
  8. The M-Theory Perspective
  9. Non-Higgsable Clusters
  10. Non-Higgsable Clusters Without Torsion
  11. Non-Higgsable Clusters With Torsion
  12. Non-Simply-Connected SCM
  13. Torsion and SCM
  14. Example: Flavor Groups vs Algebras
  15. Singular Discriminant Components and Resolutions
  16. ...and 18 more sections

Figures (6)

  • Figure 1: M-theory setup for a higher-rank E-string theory and its F-theory geometry.
  • Figure 2: M-theory setup for a superconformal matter.
  • Figure 3: Realization of the orbi-instanton theory in M-theory on the partial tensor branch.
  • Figure 4: 4-chain on which the M-theory flux $G_4$ evaluates to the fractional instanton number, i.e. the number of M5-branes.
  • Figure 5: Gauge algebra and matter content for single-curve NHCs.
  • ...and 1 more figures