A proof of all ranks S-duality conjecture for K3 surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913506718121984 |
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| author | Jiang, Yunfeng Tseng, Hsian-Hua |
| author_facet | Jiang, Yunfeng Tseng, Hsian-Hua |
| contents | Using the multiple cover formula of Y. Toda for counting invariants of semistable twisted sheaves over twisted local K3 surfaces we calculate the $\SU(r)/\zz_r$-Vafa-Witten invariants for K3 surfaces for any rank $r$ for the Langlands dual group $\SU(r)/\zz_r$ of the gauge group $\SU(r)$. We generalize and prove the S-duality conjecture of Vafa-Witten for K3 surfaces in any rank $r$ based on the result of Tanaka-Thomas for the $\SU(r)$-Vafa-Witten invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_09562 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A proof of all ranks S-duality conjecture for K3 surfaces Jiang, Yunfeng Tseng, Hsian-Hua Algebraic Geometry Symplectic Geometry Using the multiple cover formula of Y. Toda for counting invariants of semistable twisted sheaves over twisted local K3 surfaces we calculate the $\SU(r)/\zz_r$-Vafa-Witten invariants for K3 surfaces for any rank $r$ for the Langlands dual group $\SU(r)/\zz_r$ of the gauge group $\SU(r)$. We generalize and prove the S-duality conjecture of Vafa-Witten for K3 surfaces in any rank $r$ based on the result of Tanaka-Thomas for the $\SU(r)$-Vafa-Witten invariants. |
| title | A proof of all ranks S-duality conjecture for K3 surfaces |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2003.09562 |