Resurgence of Refined Topological Strings and Dual Partition Functions - Alexandrov, Sergey; Mariño, Marcos; Pioline, Boris (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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.