Magic square and half-hypermultiplets in F-theory
arXiv:2008.09272 · doi:10.1093/ptep/ptac022
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 , or , we investigate, as the final magical example, an F-theory on an elliptic fibration over a Hirzebruch surface of the non-split type, in which the unbroken gauge symmetry is supposed to be . 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 points, where half-hypermultiplets of would have appeared in the split model. We also consider the problem on the non-local matter generation near the 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.
arXiv comment18 pages, 2 figures
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