Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua
Abstract We focus on 4D N $$ \mathcal{N} $$ = 2 string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi-Yau three-fold X IIA in the Type IIA language is further assumed to have a regular K3-fibration. It is well-known that one can assign a modular form Φ to such...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP06(2020)021 |
| _version_ | 1818257642659774464 |
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| author | Yuichi Enoki Taizan Watari |
| author_facet | Yuichi Enoki Taizan Watari |
| author_sort | Yuichi Enoki |
| collection | DOAJ |
| description | Abstract We focus on 4D N $$ \mathcal{N} $$ = 2 string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi-Yau three-fold X IIA in the Type IIA language is further assumed to have a regular K3-fibration. It is well-known that one can assign a modular form Φ to such a vacuum by counting perturbative BPS states in Heterotic theory or collecting Noether-Lefschetz numbers associated with the K3-fibration of X IIA. In this article, we expand the observations and ideas (using gauge threshold correction) in the literature and formulate a modular form Ψ with full generality for the class of vacua above, which can be used along with Φ for the purpose of classification of those vacua. Topological invariants of X IIA can be extracted from Φ and Ψ, and even a pair of diffeomorphic Calabi-Yau’s with different Kähler cones may be distinguished by introducing the notion of “the set of Ψ’s for Higgs cascades/for curve classes”. We illustrated these ideas by simple examples. |
| first_indexed | 2024-12-12T17:46:54Z |
| format | Article |
| id | doaj.art-8631398c5f8b45ffbb81b918de802ee5 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T17:46:54Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8631398c5f8b45ffbb81b918de802ee52022-12-22T00:16:55ZengSpringerOpenJournal of High Energy Physics1029-84792020-06-012020616410.1007/JHEP06(2020)021Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacuaYuichi Enoki0Taizan Watari1Kavli Institute for the Physics and Mathematics of the Universe (WPI), the University of TokyoKavli Institute for the Physics and Mathematics of the Universe (WPI), the University of TokyoAbstract We focus on 4D N $$ \mathcal{N} $$ = 2 string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi-Yau three-fold X IIA in the Type IIA language is further assumed to have a regular K3-fibration. It is well-known that one can assign a modular form Φ to such a vacuum by counting perturbative BPS states in Heterotic theory or collecting Noether-Lefschetz numbers associated with the K3-fibration of X IIA. In this article, we expand the observations and ideas (using gauge threshold correction) in the literature and formulate a modular form Ψ with full generality for the class of vacua above, which can be used along with Φ for the purpose of classification of those vacua. Topological invariants of X IIA can be extracted from Φ and Ψ, and even a pair of diffeomorphic Calabi-Yau’s with different Kähler cones may be distinguished by introducing the notion of “the set of Ψ’s for Higgs cascades/for curve classes”. We illustrated these ideas by simple examples.http://link.springer.com/article/10.1007/JHEP06(2020)021String DualitySuperstrings and Heterotic StringsDifferential and Algebraic GeometryTopological Strings |
| spellingShingle | Yuichi Enoki Taizan Watari Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua Journal of High Energy Physics String Duality Superstrings and Heterotic Strings Differential and Algebraic Geometry Topological Strings |
| title | Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua |
| title_full | Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua |
| title_fullStr | Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua |
| title_full_unstemmed | Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua |
| title_short | Modular forms as classification invariants of 4D N $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua |
| title_sort | modular forms as classification invariants of 4d n mathcal n 2 heterotic iia dual vacua |
| topic | String Duality Superstrings and Heterotic Strings Differential and Algebraic Geometry Topological Strings |
| url | http://link.springer.com/article/10.1007/JHEP06(2020)021 |
| work_keys_str_mv | AT yuichienoki modularformsasclassificationinvariantsof4dnmathcaln2heteroticiiadualvacua AT taizanwatari modularformsasclassificationinvariantsof4dnmathcaln2heteroticiiadualvacua |