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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/2407.04483 |
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| _version_ | 1866915673472499712 |
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| author | Hao, Qianyu Neitzke, Andrew |
| author_facet | Hao, Qianyu Neitzke, Andrew |
| contents | We introduce a nonabelianization map for conformal blocks, which relates $c=1$ Virasoro blocks on a Riemann surface $C$ to Heisenberg blocks on a branched double cover $\widetilde{C}$ of $C$. The nonabelianization map uses the datum of a spectral network on $C$. It gives new formulas for Virasoro blocks in terms of fermion correlation functions determined by the Heisenberg block. The nonabelianization map also intertwines with the action of Verlinde loop operators, and can be used to construct eigenblocks. This leads to new Kyiv-type formulas and regularized Fredholm determinant formulas for $τ$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new construction of $c=1$ Virasoro blocks Hao, Qianyu Neitzke, Andrew High Energy Physics - Theory Mathematical Physics Algebraic Geometry We introduce a nonabelianization map for conformal blocks, which relates $c=1$ Virasoro blocks on a Riemann surface $C$ to Heisenberg blocks on a branched double cover $\widetilde{C}$ of $C$. The nonabelianization map uses the datum of a spectral network on $C$. It gives new formulas for Virasoro blocks in terms of fermion correlation functions determined by the Heisenberg block. The nonabelianization map also intertwines with the action of Verlinde loop operators, and can be used to construct eigenblocks. This leads to new Kyiv-type formulas and regularized Fredholm determinant formulas for $τ$-functions. |
| title | A new construction of $c=1$ Virasoro blocks |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2407.04483 |