Geometric constraints in dual F-theory and heterotic string compactifications
Name
Anderson-2014-Geometric constraint.pdf
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1.17 MB
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Author(s)
Anderson, Lara B.
Taylor, Washington
Date Issued
August 2014
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Citation
Anderson, Lara B., and Washington Taylor. “Geometric Constraints in Dual F-Theory and Heterotic String Compactifications.” J. High Energ. Phys. 2014, no. 8 (August 2014).
Version
Final published version
Abstract
We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. Specifically, we give a complete classification of models where the heterotic theory is compactified on a smooth Calabi-Yau threefold that is elliptically fibered with a single section and carries smooth irreducible vector bundles, and the dual F-theory model has a corresponding threefold base that has the form of a ℙ[superscript 1] bundle. We formulate simple conditions for the geometry on the F-theory side to support an elliptically fibered Calabi-Yau fourfold. We match these conditions with conditions for the existence of stable vector bundles on the heterotic side, and show that F-theory gives new insight into the conditions under which such bundles can be constructed. In particular, we find that many allowed F-theory models correspond to vector bundles on the heterotic side with exceptional structure groups, and determine a topological condition that is only satisfied for bundles of this type. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all (4962) F-theory threefold bases for dual F-theory/heterotic constructions in the subset of models where the common twofold base surface is toric, and give both toric and non-toric examples of the general results.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP08(2014)025
