Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces

TL;DR

This paper shows how non-simply-laced gauge and flavor symmetries naturally emerge in F-theory through complex structure deformations and brane splitting, leading to new insights into 4d SCFTs with such symmetries.

Contribution

It introduces a geometric mechanism for generating non-simply-laced symmetries in F-theory via Calabi-Yau deformations and brane monodromies, expanding understanding of singular space compactifications.

Findings

Non-simply-laced symmetries arise from complex structure deformations.

Splitting of seven-branes creates new geometric loops affecting monodromy.

Collision of D3-brane with seven-brane yields 4d N=1 SCFT with non-simply-laced flavor symmetry.

Abstract

We demonstrate how non-simply-laced gauge and flavor symmetries arise in F-theory on spaces with non-isolated singularities. The breaking from a simply-laced symmetry to one that is non-simply-laced is induced by Calabi-Yau complex structure deformation. In all examples the deformation maintains non-isolated singularities but is accompanied by a splitting of an I1 seven-brane that opens new loops in the geometry near a non-abelian seven-brane. The splitting also arises in the moduli space of a probe D3-brane, which upon traversing the new loop experiences a monodromy that acts on 3-7 string junctions on the singular space. The monodromy reduces the symmetry algebra, which is the flavor symmetry of the D3-brane and the gauge symmetry of the seven-brane, to one that is non-simply-laced. A collision of the D3-brane with the seven-brane gives rise to a 4d N = 1 SCFT with a non-simply-laced flavor symmetry.