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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.07299 |
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| _version_ | 1866908854915170304 |
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| author | Debray, Arun Yu, Matthew |
| author_facet | Debray, Arun Yu, Matthew |
| contents | We look at a new string$^h$ tangential structure first introduced by Devalapurkar and relate it to the $W_7=0$ condition of Diaconescu-Moore-Witten for type IIA string theory and M-theory. We show that a string$^h$ structure on the target space automatically satisfies the $W_7=0$ condition and we also explain when the $W_7=0$ condition gives rise to a string$^h$ structure. Devalapurkar initially constructed $MString^h$ in such a way that it orients $tmf_1(3)$; we extend Devalapurkar's result, showing that $MString^h$ orients $tmf_1(n)$. We compute the homotopy groups of $MString^h$ in the dimensions relevant for physical applications, and apply them to anomaly cancellation applications for certain compactifications of type IIA string theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Type IIA String Theory and tmf with Level Structure Debray, Arun Yu, Matthew Algebraic Topology High Energy Physics - Theory Mathematical Physics 55P42, 55P43 We look at a new string$^h$ tangential structure first introduced by Devalapurkar and relate it to the $W_7=0$ condition of Diaconescu-Moore-Witten for type IIA string theory and M-theory. We show that a string$^h$ structure on the target space automatically satisfies the $W_7=0$ condition and we also explain when the $W_7=0$ condition gives rise to a string$^h$ structure. Devalapurkar initially constructed $MString^h$ in such a way that it orients $tmf_1(3)$; we extend Devalapurkar's result, showing that $MString^h$ orients $tmf_1(n)$. We compute the homotopy groups of $MString^h$ in the dimensions relevant for physical applications, and apply them to anomaly cancellation applications for certain compactifications of type IIA string theory. |
| title | Type IIA String Theory and tmf with Level Structure |
| topic | Algebraic Topology High Energy Physics - Theory Mathematical Physics 55P42, 55P43 |
| url | https://arxiv.org/abs/2411.07299 |