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, Δ) 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 e 7 × s u 2 $$ {\mathfrak{e}}_7\times \mathfrak{s}{\mathfrak{u}}_2 $$ and e 6 × s u 3 $$ {\mathfrak{e}}_6\times \mathfrak{s}{\mathfrak{u}}_3 $$ , 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 s u 2 $$ \mathfrak{s}{\mathfrak{u}}_2 $$ and the three-index symmetric representation of s u 3 $$ \mathfrak{s}{\mathfrak{u}}_3 $$ , and after further higgsing can yield discrete non-abelian symmetries