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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2311.17638 |
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| _version_ | 1866910556631334912 |
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| author | Alexandrov, Sergey Mariño, Marcos Pioline, Boris |
| author_facet | Alexandrov, Sergey Mariño, Marcos Pioline, Boris |
| contents | We study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $\mathsf{b}$. For $\mathsf{b}\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $\mathsf{b}$ and $1/\mathsf{b}$. We show that the corresponding Stokes automorphism is expressed in terms of a generalization of the non-compact quantum dilogarithm, and we conjecture that the Stokes constants are determined by the refined Donaldson-Thomas invariants counting spin-$j$ BPS states. This jump in the refined topological string partition function is a special case (unit five-brane charge) of a more general transformation property of wave functions on quantum twisted tori introduced in earlier work by two of the authors. We show that this property follows from the transformation of a suitable refined dual partition function across BPS rays, defined by extending the Moyal star product to the realm of contact geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Resurgence of Refined Topological Strings and Dual Partition Functions Alexandrov, Sergey Mariño, Marcos Pioline, Boris High Energy Physics - Theory Mathematical Physics We study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $\mathsf{b}$. For $\mathsf{b}\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $\mathsf{b}$ and $1/\mathsf{b}$. We show that the corresponding Stokes automorphism is expressed in terms of a generalization of the non-compact quantum dilogarithm, and we conjecture that the Stokes constants are determined by the refined Donaldson-Thomas invariants counting spin-$j$ BPS states. This jump in the refined topological string partition function is a special case (unit five-brane charge) of a more general transformation property of wave functions on quantum twisted tori introduced in earlier work by two of the authors. We show that this property follows from the transformation of a suitable refined dual partition function across BPS rays, defined by extending the Moyal star product to the realm of contact geometry. |
| title | Resurgence of Refined Topological Strings and Dual Partition Functions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.17638 |