Magic square and half-hypermultiplets in F-theory

Abstract

In six-dimensional F-theory/heterotic string theory, half-hypermultiplets arise only when they correspond to particular quaternionic Kähler symmetric spaces, which are mostly associated with the Freudenthal-Tits magic square. Motivated by the intriguing singularity structure previously found in such F-theory models with a gauge group $SU(6)$,$SO(12)$ or $E_7$, we investigate, as the final magical example, an F-theory on an elliptic fibration over a Hirzebruch surface of the non-split $I_6$ type, in which the unbroken gauge symmetry is supposed to be $Sp(3)$. We find significant qualitative differences between the previous F-theory models associated with the magic square and the present case. We argue that the relevant half-hypermultiplets arise at the $E_6$ points, where half-hypermultiplets $20$ of $SU(6)$ would have appeared in the split model. We also consider the problem on the non-local matter generation near the $D_6$ point. After stating what the problem is, we explain why this is so by using the recent result that a split/non-split transition can be regarded as a conifold transition.

18 pages, 2 figures

References in corpus (5)

• F-theory Family Unification
• Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I
• More on a dessin on the base: Kodaira exceptional fibers and mutually (non-)local branes
• Looijenga's weighted projective space, Tate's algorithm and Mordell-Weil Lattice in F-theory and heterotic string theory
• Non-split singularities and conifold transitions in F-theory

Cited by in corpus (2)

• Non-split singularities and conifold transitions in F-theory
• New perspectives in the duality of M-theory, heterotic strings, and F-theory