Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models
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...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/105760 https://orcid.org/0000-0001-8566-6706 |
| _version_ | 1811089614486634496 |
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| author | Klevers, Denis Taylor IV, Washington |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Klevers, Denis Taylor IV, Washington |
| author_sort | Klevers, Denis |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:22:00Z |
| format | Article |
| id | mit-1721.1/105760 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:22:00Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1057602022-10-01T20:52:36Z Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models Klevers, Denis Taylor IV, Washington Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Taylor IV, Washington 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. United States. Dept. of Energy (contract #DE-SC00012567) 2016-12-08T21:38:47Z 2016-12-08T21:38:47Z 2016-06 2016-04 2016-07-01T03:27:52Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/105760 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. https://orcid.org/0000-0001-8566-6706 en http://dx.doi.org/10.1007/JHEP06(2016)171 Journal of High Energy Physics Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Klevers, Denis Taylor IV, Washington Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title | Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title_full | Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title_fullStr | Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title_full_unstemmed | Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title_short | Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models |
| title_sort | three index symmetric matter representations of su 2 in f theory from non tate form weierstrass models |
| url | http://hdl.handle.net/1721.1/105760 https://orcid.org/0000-0001-8566-6706 |
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