A proof of a conjecture of Gukov-Pei-Putrov-Vafa
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912011456086016 |
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| author | Murakami, Yuya |
| author_facet | Murakami, Yuya |
| contents | In this paper, we prove Gukov-Pei-Putrov-Vafa's conjecture that the Witten-Reshetikhin-Turaev invariants are radial limits of homological blocks, which are $ q $-series introduced by them for plumbed $ 3 $-manifolds with negative definite linking matrices. In our previous work, the author attributed this conjecture to the holomorphy of certain rational functions by developing an asymptotic formula based on the Euler-Maclaurin summation formula. However, it is challenging to prove holomorphy for general plumbed manifolds. In this paper, we address this challenge using induction on a sequence of trees obtained by repeating "pruning trees." |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13526 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A proof of a conjecture of Gukov-Pei-Putrov-Vafa Murakami, Yuya Geometric Topology High Energy Physics - Theory Mathematical Physics Number Theory Quantum Algebra 57K31, 57K10, 57K16, 11F27, 11L05, 11T24 In this paper, we prove Gukov-Pei-Putrov-Vafa's conjecture that the Witten-Reshetikhin-Turaev invariants are radial limits of homological blocks, which are $ q $-series introduced by them for plumbed $ 3 $-manifolds with negative definite linking matrices. In our previous work, the author attributed this conjecture to the holomorphy of certain rational functions by developing an asymptotic formula based on the Euler-Maclaurin summation formula. However, it is challenging to prove holomorphy for general plumbed manifolds. In this paper, we address this challenge using induction on a sequence of trees obtained by repeating "pruning trees." |
| title | A proof of a conjecture of Gukov-Pei-Putrov-Vafa |
| topic | Geometric Topology High Energy Physics - Theory Mathematical Physics Number Theory Quantum Algebra 57K31, 57K10, 57K16, 11F27, 11L05, 11T24 |
| url | https://arxiv.org/abs/2302.13526 |