期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 12, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP12(2016)031
关键词
Differential and Algebraic Geometry; F-Theory; Global Symmetries; String Duality
资金
- Bonn-Cologne Graduate School BCGS
- Deutsche Forschungsgemeinschaft [SFB-Transregio TR33]
- European Union [PITN-GA-2009-237920]
- NSF [PHY-1417337, PHY-1417316]
- KIAS
- Division Of Physics
- Direct For Mathematical & Physical Scien [1417337] Funding Source: National Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1417316] Funding Source: National Science Foundation
We give further evidence that genus-one fibers with multi-sections are mirror dual to fibers with Mordell-Weil torsion. In the physics of F-theory compactifications this implies a relation between models with a non-simply connected gauge group and those with discrete symmetries. We provide a combinatorial explanation of this phenomenon for toric hypersurfaces. In particular this leads to a criterion to deduce Mordell-Weil torsion directly from the polytope. For all 3134 complete intersection genus-one curves in three-dimensional toric ambient spaces we confirm the conjecture by explicit calculation. We comment on several new features of these models: the Weierstrass forms of many models can be identified by relabeling the coefficient sections. This reduces the number of models to 1024 inequivalent ones. We give an example of a fiber which contains only non-toric sections one of which becomes toric when the fiber is realized in a different ambient space. Similarly a singularity in codimension one can have a toric resolution in one representation while it is non-toric in another. Finally we give a list of 24 inequivalent genus-one fibers that simultaneously exhibit multi-sections and Mordell-Weil torsion in the Jacobian. We discuss a self-mirror example from this list in detail.
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