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

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.

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• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• T-Branes, String Junctions, and 6D SCFTs
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• Magic square and half-hypermultiplets in F-theory
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• Non-split singularities and conifold transitions in F-theory