Resurgence of Refined Topological Strings and Dual Partition Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Alexandrov, Sergey, Mariño, Marcos, Pioline, Boris
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212347
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Resurgence of Refined Topological Strings and Dual Partition Functions. Sergey Alexandrov, Marcos Mariño and Boris Pioline. SIGMA 20 (2024), 073, 34 pages

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.