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 $\times$ 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 $\times$ 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 $\times$ K3 constructed does not have a section, gauge groups arising on 7-branes for F-theory models on constructed K3 $\times$ K3's do not have $U(1)$-part. Interestingly, exceptional gauge group $E_6$ appears for some cases.
Highlights
JHEP03(2016)042 section to the fibration only form a special subset
Calabi-Yau 4-fold, for the reason that the techniques from algebraic geometry enable to perform a detailed analysis of F-theory compactifications on K3 × K3
When more than two αi ’s coincide, the equation (3.1) does not give a K3 surface. In this way we find that singular fibers of Fermat type K3 surface S defined by the equation (3.1) are located at t = αi, i = 1, · · ·, 6, and when αi ’s are mutually distinct, their fiber types are all IV
Summary
JHEP03(2016) section to the fibration only form a special subset. F-theory compactifications on elliptic manifolds without a section was considered in [17]. By construction, such K3 × K3 does not admit a section. To study F-theory compactifications on a class of K3 × K3 without a section in detail, we limit ourselves to consider two specific families of K3 surfaces, among hypersurfaces of bidegree (2,3) in P1 × P2. These K3 surfaces do not have a section, so the gauge groups which arise on 7-branes do not have U(1)-factor
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