The magic square and half-hypermultiplets in F-theory

• Main Authors: Kuramochi, R. (Author), Mizoguchi, S. (Author), Tani, T. (Author)
• Format: Article
• Language: English
• Published: Physical Society of Japan 2022
• Subjects: B29; B80
• Online Access: View Fulltext in Publisher

 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 E7, we investigate, as the final magical example, an F-theory on an elliptic fibration over a Hirzebruch surface of the non-split I6 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 E6 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 D6 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. © 2022 The Author(s) 2022. Published by Oxford University Press on behalf of the Physical Society of Japan.