Abstract
We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau d-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary polytope. In particular for fibers that generically lead to multiple sections, only multi-sections or that are complete intersections in higher codimension, our technique is vastly more efficient than classical approaches. As an application we study two Higgs chains of six-dimensional supergravities that are engineered by fibrations of codimension two complete intersection fibers. Both chains end on a vacuum with G = ℤ4 that is engineered by fibrations of bi-quadrics in ℙ3. We use the detailed knowledge of the structure of the reducible fibers that we obtain from GV-spectroscopy to comment on the corresponding Tate-Shafarevich group. We also show that for all fibers the six-dimensional supergravity anomalies including the discrete anomalies generically cancel.
Highlights
F-theory provides a powerful dictionary between non-perturbative type IIB string compactifications and the geometry of genus one fibered Calabi-Yau manifolds [1,2,3]
We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces
In this work we have presented a novel technique to determine base independent expressions for the matter loci of families of complete intersection fibers in toric ambient spaces
Summary
F-theory provides a powerful dictionary between non-perturbative type IIB string compactifications and the geometry of genus one fibered Calabi-Yau manifolds [1,2,3]. The resulting fiber GV invariants are polynomials in the Chern classes of the line bundles and the base and provide the base independent fibration data This technique, which we refer to as GV-spectroscopy, provides a very efficient way to obtain the fibration data for complete intersection fibers in toric ambient spaces. The application of GV-spectroscopy is easy when the fiber leads to a small gauge group G During our work on this project we learned of [22] which has some overlap
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