Orders of vanishing and U(1) charges in F-theory
Abstract Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2022)051 |
| _version_ | 1819123805940875264 |
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| author | Nikhil Raghuram Andrew P. Turner |
| author_facet | Nikhil Raghuram Andrew P. Turner |
| author_sort | Nikhil Raghuram |
| collection | DOAJ |
| description | Abstract Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange [1]. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland. |
| first_indexed | 2024-12-22T07:14:12Z |
| format | Article |
| id | doaj.art-9b84e3cb4ce24d13b168c7bec76bdeaa |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T07:14:12Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9b84e3cb4ce24d13b168c7bec76bdeaa2022-12-21T18:34:26ZengSpringerOpenJournal of High Energy Physics1029-84792022-03-0120223112010.1007/JHEP03(2022)051Orders of vanishing and U(1) charges in F-theoryNikhil Raghuram0Andrew P. Turner1Department of Physics, Robeson Hall, 0435 Virginia TechDepartment of Physics and Astronomy, University of PennsylvaniaAbstract Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange [1]. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland.https://doi.org/10.1007/JHEP03(2022)051F-TheoryGauge Symmetry |
| spellingShingle | Nikhil Raghuram Andrew P. Turner Orders of vanishing and U(1) charges in F-theory Journal of High Energy Physics F-Theory Gauge Symmetry |
| title | Orders of vanishing and U(1) charges in F-theory |
| title_full | Orders of vanishing and U(1) charges in F-theory |
| title_fullStr | Orders of vanishing and U(1) charges in F-theory |
| title_full_unstemmed | Orders of vanishing and U(1) charges in F-theory |
| title_short | Orders of vanishing and U(1) charges in F-theory |
| title_sort | orders of vanishing and u 1 charges in f theory |
| topic | F-Theory Gauge Symmetry |
| url | https://doi.org/10.1007/JHEP03(2022)051 |
| work_keys_str_mv | AT nikhilraghuram ordersofvanishingandu1chargesinftheory AT andrewpturner ordersofvanishingandu1chargesinftheory |