Resurgence of Refined Topological Strings and Dual Partition Functions

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 ₛ and fixed refinement parameter b. For ≠ 1, the Borel transform admits two families of simple poles, corresponding to integra...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автори: Alexandrov, Sergey, Mariño, Marcos, Pioline, Boris
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/212347
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Resurgence of Refined Topological Strings and Dual Partition Functions. Sergey Alexandrov, Marcos Mariño and Boris Pioline. SIGMA 20 (2024), 073, 34 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме: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 ₛ and fixed refinement parameter b. For ≠ 1, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by and 1/. 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- 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.
ISSN:1815-0659