Abstract
We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a structure invariant under a single C∗ action (sometimes called “T-varieties” in the mathematical literature) that can act as bases for an elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404 distinct bases, which include as a subset the previously studied set of strictly toric bases. Calabi-Yau threefolds constructed in this fashion include examples with previously unknown Hodge numbers. There are also bases over which the generic elliptic fibration has a Mordell-Weil group of sections with nonzero rank, corresponding to non-Higgsable U(1) factors in the 6D supergravity model; this type of structure does not arise for generic elliptic fibrations in the purely toric context.
Highlights
While mathematicians and physicists have used many methods to construct and study Calabi-Yau threefolds, one of the main approaches that has been fruitful for systematically classifying large numbers of Calabi-Yau geometries is the mathematical framework of toric geometry [7]
For any base surface B, the structure of non-Higgsable clusters determines the minimal nonabelian gauge group and matter content of the 6D supergravity theory corresponding to a generic elliptic fibration with section over B
In this paper we have initiated a systematic study of a class of geometries for the bases of elliptically fibered Calabi-Yau threefolds that goes beyond the framework of toric geometry widely used in previous work
Summary
A general approach to systematically classifying base surfaces B for 6D F-theory compactifications was developed in [10] This approach is based on identifying irreducible components in the structure of effective divisors on B, composed of intersecting combinations of curves of negative self-intersection over which the generic elliptic fibration is singular. For any base surface B, the structure of non-Higgsable clusters determines the minimal nonabelian gauge group and matter content of the 6D supergravity theory corresponding to a generic elliptic fibration with section over B. In [12], the complete set of toric bases was constructed in this fashion, and in this paper we carry out the analogous construction for C∗-bases
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