Tate’s algorithm for F-theory GUTs with two U(1)s

Craig Lawrie; Damiano Sacco

doi:10.1007/JHEP03(2015)055

Tate’s algorithm for F-theory GUTs with two U(1)s

Craig Lawrie, Damiano Sacco

Mathematics

King's College London

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Abstract: We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1)² fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate’s algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P². In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.

Original language	English
Pages (from-to)	1-53
Number of pages	53
Journal	Journal of High Energy Physics
Volume	2015
Issue number	3
DOIs	https://doi.org/10.1007/JHEP03(2015)055
Publication status	Published - 2015

Keywords

Differential and Algebraic Geometry
F-Theory

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10.1007/JHEP03(2015)055

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abstract = "Abstract: We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1)2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate{\textquoteright}s algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P2. In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.",

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AU - Lawrie, Craig

AU - Sacco, Damiano

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N2 - Abstract: We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1)2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate’s algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P2. In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.

AB - Abstract: We present a systematic study of elliptic fibrations for F-theory realizations of gauge theories with two U(1) factors. In particular, we determine a new class of SU(5) × U(1)2 fibrations, which can be used to engineer Grand Unified Theories, with multiple, differently charged, 10 matter representations. To determine these models we apply Tate’s algorithm to elliptic fibrations with two U(1) symmetries, which are realized in terms of a cubic in P2. In the process, we find fibers which are not characterized solely in terms of vanishing orders, but with some additional specialization, which plays a key role in the construction of these novel SU(5) models with multiple 10 matter. We also determine a table of Tate-like forms for Kodaira fibers with two U(1)s.

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KW - F-Theory

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DO - 10.1007/JHEP03(2015)055

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JO - Journal of High Energy Physics

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ER -

Tate’s algorithm for F-theory GUTs with two U(1)s

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Keywords

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