Abstract
We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 × K3, with one of the K3’s chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 × K3’s.
We determine the gauge groups and matter fields which arise on 7-branes for these models of F-theory compactifications without a section. Since each K3 × K3 constructed does not have a section, gauge groups arising on 7-branes for F-theory models on constructed K3 × K3’s do not have U(1)-part. Interestingly, exceptional gauge group E 6 appears for some cases.
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Kimura, Y. Gauge groups and matter fields on some models of F-theory without section. J. High Energ. Phys. 2016, 42 (2016). https://doi.org/10.1007/JHEP03(2016)042
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DOI: https://doi.org/10.1007/JHEP03(2016)042