Chow groups, Deligne cohomology and massless matter in F-theory

We propose a method to compute the exact number of charged localized massless matter states in an F-theory compactification on a Calabi-Yau 4-fold with non-trivial 3-form data. Our starting point is the description of the 3-form data via Deligne cohomology. A refined cycle map allows us to specify c...

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Bibliographic Details
Published inarXiv.org
Main Authors Bies, Martin, Mayrhofer, Christoph, Pehle, Christian, Weigand, Timo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.02.2014
Subjects
Algorithms
Branes
Homology
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Summary:We propose a method to compute the exact number of charged localized massless matter states in an F-theory compactification on a Calabi-Yau 4-fold with non-trivial 3-form data. Our starting point is the description of the 3-form data via Deligne cohomology. A refined cycle map allows us to specify concrete elements therein in terms of the second Chow group of the 4-fold, i.e. rational equivalence classes of algebraic 2-cycles. We use intersection theory within the Chow ring to extract from this data a line bundle class on the curves in the base of the fibration on which charged matter is localized. The associated cohomology groups are conjectured to count the exact massless spectrum, in agreement with general patterns in Type IIB compactifications with 7-branes. We exemplify our approach by calculating the massless spectrum in an SU(5) x U(1) toy model based on an elliptic 4-fold with an extra section. The explicit evaluation of the cohomology classes is performed with the help of the cohomCalg-algorithm by Blumenhagen et al.
ISSN:2331-8422