Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory

Abstract

We present a prescription in F-theory for realizing matter in "exotic" representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D superconformal field theories coupled to gravity. A deformation in Higgs branch moduli space takes us to a weakly coupled gauge theory description. In the corresponding elliptically fibered Calabi--Yau threefold, the minimal Weierstrass model parameters $(f,g,\Delta )$ vanish at collisions of the discriminant at least to order $(4,6,12)$, but with sufficiently high order of tangency to ensure the existence of T-brane deformations to a weakly coupled gauge theory with exotic bifundamentals. We present explicit examples including bifundamental hypermultiplets of ${\mathfrak{e}}_7\times {\mathfrak{su}}_2$ and ${\mathfrak{e}}_6\times {\mathfrak{su}}_3$, each of which have dual heterotic orbifold descriptions. Geometrically, these matter fields are delocalized across multiple points of an F-theory geometry. Symmetry breaking with such representations can be used to produce high dimension representations of simple gauge groups such as the four-index symmetric representation of ${\mathfrak{su}}_2$ and the three-index symmetric representation of ${\mathfrak{su}}_3$, and after further higgsing can yield discrete non-abelian symmetries.

v2: 44 pages, 4 figures, typos corrected, clarifications added

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• Nilpotent Networks and 4D RG Flows
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• Geometric Unification of Higgs Bundle Vacua
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• Geometric Approaches to Quantum Fields and Strings at Strong Couplings