Sections, multisections, and U(1) fields in F-theory
© 2016, Journal of Singularities. All rights reserved. We show that genus-one fibrations lacking a global section fit naturally into the geometric moduli space of Weierstrass models. Elliptic fibrations with multiple sections (nonzero Mordell-Weil rank), which give rise in F-theory to abelian U(1) f...
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| Format: | Article |
| Language: | English |
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Journal of Singularities
2021
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| Online Access: | https://hdl.handle.net/1721.1/134521 |
| _version_ | 1826212047718711296 |
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| author | Morrison, David Taylor, Washington |
| author_facet | Morrison, David Taylor, Washington |
| author_sort | Morrison, David |
| collection | MIT |
| description | © 2016, Journal of Singularities. All rights reserved. We show that genus-one fibrations lacking a global section fit naturally into the geometric moduli space of Weierstrass models. Elliptic fibrations with multiple sections (nonzero Mordell-Weil rank), which give rise in F-theory to abelian U(1) fields, arise as a subspace of the set of genus-one fibrations with multisections. Higgsing of certain matter multiplets charged under abelian gauge fields in the corresponding supergravity theories break the U(1) gauge symmetry to a discrete gauge symmetry group. We demonstrate these results explicitly in the case of bisections, and describe the general framework for multisections of higher degree. We further show that nearly every U(1) gauge symmetry arising in an Ftheory model can be “unHiggsed” to an SU(2) gauge symmetry with adjoint matter, though in certain situations this leads to a model in which a superconformal field theory is coupled to a conventional gauge and gravity theory. The only exceptions are cases in which the attempted unHiggsing leads to a boundary point at an infinite distance from the interior of the moduli space. |
| first_indexed | 2024-09-23T15:15:18Z |
| format | Article |
| id | mit-1721.1/134521 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:15:18Z |
| publishDate | 2021 |
| publisher | Journal of Singularities |
| record_format | dspace |
| spelling | mit-1721.1/1345212021-10-28T03:24:58Z Sections, multisections, and U(1) fields in F-theory Morrison, David Taylor, Washington © 2016, Journal of Singularities. All rights reserved. We show that genus-one fibrations lacking a global section fit naturally into the geometric moduli space of Weierstrass models. Elliptic fibrations with multiple sections (nonzero Mordell-Weil rank), which give rise in F-theory to abelian U(1) fields, arise as a subspace of the set of genus-one fibrations with multisections. Higgsing of certain matter multiplets charged under abelian gauge fields in the corresponding supergravity theories break the U(1) gauge symmetry to a discrete gauge symmetry group. We demonstrate these results explicitly in the case of bisections, and describe the general framework for multisections of higher degree. We further show that nearly every U(1) gauge symmetry arising in an Ftheory model can be “unHiggsed” to an SU(2) gauge symmetry with adjoint matter, though in certain situations this leads to a model in which a superconformal field theory is coupled to a conventional gauge and gravity theory. The only exceptions are cases in which the attempted unHiggsing leads to a boundary point at an infinite distance from the interior of the moduli space. 2021-10-27T20:05:24Z 2021-10-27T20:05:24Z 2016 2019-06-17T23:06:14Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134521 en 10.5427/JSING.2016.15G Journal of Singularities Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Journal of Singularities arXiv |
| spellingShingle | Morrison, David Taylor, Washington Sections, multisections, and U(1) fields in F-theory |
| title | Sections, multisections, and U(1) fields in F-theory |
| title_full | Sections, multisections, and U(1) fields in F-theory |
| title_fullStr | Sections, multisections, and U(1) fields in F-theory |
| title_full_unstemmed | Sections, multisections, and U(1) fields in F-theory |
| title_short | Sections, multisections, and U(1) fields in F-theory |
| title_sort | sections multisections and u 1 fields in f theory |
| url | https://hdl.handle.net/1721.1/134521 |
| work_keys_str_mv | AT morrisondavid sectionsmultisectionsandu1fieldsinftheory AT taylorwashington sectionsmultisectionsandu1fieldsinftheory |