Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
Abstract We show that the elliptic genus of the higher rank E-strings can be computed based solely on the genus 0 Gromov-Witten invariants of the corresponding elliptic geometry. To set up our computation, we study the structure of the topological string free energy on elliptically fibered Calabi-Ya...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2019)078 |
| _version_ | 1818851771075788800 |
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| author | Zhihao Duan Jie Gu Amir-Kian Kashani-Poor |
| author_facet | Zhihao Duan Jie Gu Amir-Kian Kashani-Poor |
| author_sort | Zhihao Duan |
| collection | DOAJ |
| description | Abstract We show that the elliptic genus of the higher rank E-strings can be computed based solely on the genus 0 Gromov-Witten invariants of the corresponding elliptic geometry. To set up our computation, we study the structure of the topological string free energy on elliptically fibered Calabi-Yau manifolds both in the unrefined and the refined case, determining the maximal amount of the modular structure of the partition function that can be salvaged. In the case of fibrations exhibiting only isolated fibral curves, we show that the principal parts of the topological string partition function at given base-wrapping can be computed from the knowledge of the genus 0 Gromov-Witten invariants at this base-wrapping, and the partition function at lower base-wrappings. For the class of geometries leading to the higher rank E-strings, this leads to the result stated in the opening sentence. |
| first_indexed | 2024-12-19T07:10:19Z |
| format | Article |
| id | doaj.art-e2b09a519ca9498b89e01cd493e8fadf |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T07:10:19Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e2b09a519ca9498b89e01cd493e8fadf2022-12-21T20:31:12ZengSpringerOpenJournal of High Energy Physics1029-84792019-03-012019313710.1007/JHEP03(2019)078Computing the elliptic genus of higher rank E-strings from genus 0 GW invariantsZhihao Duan0Jie Gu1Amir-Kian Kashani-Poor2LPTENS, CNRS, PSL University, Sorbonne Universités, UPMCLPTENS, CNRS, PSL University, Sorbonne Universités, UPMCLPTENS, CNRS, PSL University, Sorbonne Universités, UPMCAbstract We show that the elliptic genus of the higher rank E-strings can be computed based solely on the genus 0 Gromov-Witten invariants of the corresponding elliptic geometry. To set up our computation, we study the structure of the topological string free energy on elliptically fibered Calabi-Yau manifolds both in the unrefined and the refined case, determining the maximal amount of the modular structure of the partition function that can be salvaged. In the case of fibrations exhibiting only isolated fibral curves, we show that the principal parts of the topological string partition function at given base-wrapping can be computed from the knowledge of the genus 0 Gromov-Witten invariants at this base-wrapping, and the partition function at lower base-wrappings. For the class of geometries leading to the higher rank E-strings, this leads to the result stated in the opening sentence.http://link.springer.com/article/10.1007/JHEP03(2019)078Topological StringsF-Theory |
| spellingShingle | Zhihao Duan Jie Gu Amir-Kian Kashani-Poor Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants Journal of High Energy Physics Topological Strings F-Theory |
| title | Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants |
| title_full | Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants |
| title_fullStr | Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants |
| title_full_unstemmed | Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants |
| title_short | Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants |
| title_sort | computing the elliptic genus of higher rank e strings from genus 0 gw invariants |
| topic | Topological Strings F-Theory |
| url | http://link.springer.com/article/10.1007/JHEP03(2019)078 |
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