Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models
Abstract Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their ass...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2022)143 |
| _version_ | 1811208608105365504 |
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| author | Seung-Joo Lee Timo Weigand |
| author_facet | Seung-Joo Lee Timo Weigand |
| author_sort | Seung-Joo Lee |
| collection | DOAJ |
| description | Abstract Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in the companion paper [1]. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra. |
| first_indexed | 2024-04-12T04:24:29Z |
| format | Article |
| id | doaj.art-5cdee701c8ec4ea2afdea44b7888d1b8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-12T04:24:29Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5cdee701c8ec4ea2afdea44b7888d1b82022-12-22T03:48:07ZengSpringerOpenJournal of High Energy Physics1029-84792022-09-012022917810.1007/JHEP09(2022)143Elliptic K3 surfaces at infinite complex structure and their refined Kulikov modelsSeung-Joo Lee0Timo Weigand1Center for Theoretical Physics of the Universe, Institute for Basic ScienceInstitut für Theoretische Physik, Universität HamburgAbstract Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in the companion paper [1]. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra.https://doi.org/10.1007/JHEP09(2022)143Differential and Algebraic GeometryF-Theory |
| spellingShingle | Seung-Joo Lee Timo Weigand Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models Journal of High Energy Physics Differential and Algebraic Geometry F-Theory |
| title | Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models |
| title_full | Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models |
| title_fullStr | Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models |
| title_full_unstemmed | Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models |
| title_short | Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models |
| title_sort | elliptic k3 surfaces at infinite complex structure and their refined kulikov models |
| topic | Differential and Algebraic Geometry F-Theory |
| url | https://doi.org/10.1007/JHEP09(2022)143 |
| work_keys_str_mv | AT seungjoolee elliptick3surfacesatinfinitecomplexstructureandtheirrefinedkulikovmodels AT timoweigand elliptick3surfacesatinfinitecomplexstructureandtheirrefinedkulikovmodels |