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Resurgence of Refined Topological Strings and Dual Partition Functions
Sergey Alexandrova, Marcos Mariñob, Boris Piolinec a Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, F-34095, Montpellier, France
b Département de Physique Théorique et Section de Mathématiques, Université de Genéve, Genéve, CH-1211 Switzerland
c Laboratoire de Physique Théorique et Hautes Energies (LPTHE), UMR 7589, CNRS-Sorbonne Université, Campus Pierre et Marie Curie, 4 place Jussieu, F-75005 Paris, France
Аннотация:
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.
Ключевые слова:
resurgence, topological string theory, Borel resummation, Stokes automorphism.
Поступила: 13 декабря 2023 г.; в окончательном варианте 2 августа 2024 г.; опубликована 6 августа 2024 г.
Образец цитирования:
Sergey Alexandrov, Marcos Mariño, Boris Pioline, “Resurgence of Refined Topological Strings and Dual Partition Functions”, SIGMA, 20 (2024), 073, 34 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma2075 https://www.mathnet.ru/rus/sigma/v20/p73
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