Matter from multiply enhanced singularities in F-theory

Abstract We investigate the geometrical structure of multiply enhanced codimension-two singularities in the SU(5) model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement SU(5) → G ′ , where G ′ = E 6, E 7 or E 8,...

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Main Authors: Shun’ya Mizoguchi, Taro Tani
Format: Article
Language:English
Published: SpringerOpen 2025-03-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP03(2025)187
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author Shun’ya Mizoguchi
Taro Tani
author_facet Shun’ya Mizoguchi
Taro Tani
author_sort Shun’ya Mizoguchi
collection DOAJ
description Abstract We investigate the geometrical structure of multiply enhanced codimension-two singularities in the SU(5) model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement SU(5) → G ′ , where G ′ = E 6, E 7 or E 8, to examine whether a sufficient set of exceptional curves emerge that can explain the charged matter generation predicted from anomaly cancellation. We first apply one of the six Esole-Yau small resolutions to the multiply enhanced singularities, but it turns out that the proper transform of the threefold equation does not reflect changes in the singularity or how the generic codimension-two singularities gather there. We then use a(n) (apparently) different way of small resolutions than Esole-Yau to find that, except for the cases of G ′ = E 6 and special cases of E 7, either (1) the resolution only yields exceptional curves that are insufficient to cancel the anomaly, or (2) there arises a type of singularity that is neither a conifold nor a generalized conifold singularity. Finally, we revisit the Esole-Yau small resolution and show that the change of the way of small resolutions amounts to simply exchanging the proper transform and the constraint condition, and under this exchange the two ways of small resolutions are completely equivalent.
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spelling doaj-art-0fe12b31407948938bf8ebc34e13f5532025-08-20T03:10:05ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025314510.1007/JHEP03(2025)187Matter from multiply enhanced singularities in F-theoryShun’ya Mizoguchi0Taro Tani1Theory Center, Institute of Particle and Nuclear Studies, KEKNational Institute of Technology, Kurume CollegeAbstract We investigate the geometrical structure of multiply enhanced codimension-two singularities in the SU(5) model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement SU(5) → G ′ , where G ′ = E 6, E 7 or E 8, to examine whether a sufficient set of exceptional curves emerge that can explain the charged matter generation predicted from anomaly cancellation. We first apply one of the six Esole-Yau small resolutions to the multiply enhanced singularities, but it turns out that the proper transform of the threefold equation does not reflect changes in the singularity or how the generic codimension-two singularities gather there. We then use a(n) (apparently) different way of small resolutions than Esole-Yau to find that, except for the cases of G ′ = E 6 and special cases of E 7, either (1) the resolution only yields exceptional curves that are insufficient to cancel the anomaly, or (2) there arises a type of singularity that is neither a conifold nor a generalized conifold singularity. Finally, we revisit the Esole-Yau small resolution and show that the change of the way of small resolutions amounts to simply exchanging the proper transform and the constraint condition, and under this exchange the two ways of small resolutions are completely equivalent.https://doi.org/10.1007/JHEP03(2025)187F-TheoryAnomalies in Field and String TheoriesDifferential and Algebraic Geometry
spellingShingle Shun’ya Mizoguchi
Taro Tani
Matter from multiply enhanced singularities in F-theory
Journal of High Energy Physics
F-Theory
Anomalies in Field and String Theories
Differential and Algebraic Geometry
title Matter from multiply enhanced singularities in F-theory
title_full Matter from multiply enhanced singularities in F-theory
title_fullStr Matter from multiply enhanced singularities in F-theory
title_full_unstemmed Matter from multiply enhanced singularities in F-theory
title_short Matter from multiply enhanced singularities in F-theory
title_sort matter from multiply enhanced singularities in f theory
topic F-Theory
Anomalies in Field and String Theories
Differential and Algebraic Geometry
url https://doi.org/10.1007/JHEP03(2025)187
work_keys_str_mv AT shunyamizoguchi matterfrommultiplyenhancedsingularitiesinftheory
AT tarotani matterfrommultiplyenhancedsingularitiesinftheory