Non-Simply-Connected Symmetries in 6D SCFTs

TL;DR

This paper explores how including torsional sections in F-theory geometries of 6D SCFTs reveals full non-Abelian symmetry groups, modifies matter representations, and impacts the tensor branch, connecting to heterotic and M-theory duals.

Contribution

It introduces torsion in F-theory geometries to determine complete non-Abelian symmetry groups and analyzes their effects on the tensor branch of 6D SCFTs.

Findings

Identification of full non-Abelian group structures with torsion

Modification of symmetry centers and matter representations

Explicit construction of tensor branches for theories with torsion

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.