Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models
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Author(s)
Klevers, Denis
Taylor IV, Washington
Date Issued
June 2016
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Klevers, Denis, and Washington Taylor. "Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models." Journal of High Energy Physics (June 2016) 2016:171.
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Final published version
Abstract
We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimen-sion two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g = 3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by “unHiggsing” a model with a U(1) gauge factor under which there is matter with charge q = 3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G[subscript 2] × SU(2) models with more conventional matter content or SU(2)[superscript 3] models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass realization in the general form found by Morrison-Park, suggesting that a generalization of that form may be needed to incorporate models with arbitrary matter representations and gauge groups localized on singular divisors.
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/JHEP06(2016)171
