%0 Unpublished work
%T Resurgence of refined topological strings and dual partition functions
%+ Laboratoire Charles Coulomb (L2C)
%+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
%A Alexandrov, Sergey
%A Marino, Marcos
%A Pioline, Boris
%8 2023-12-14
%D 2023
%Z 2311.17638
%K string, topological
%K string, partition function
%K torus, twist
%K family, 2
%K string, coupling constant
%K duality
%K noncompact
%K BPS
%K star
%K Calabi-Yau
%K pole
%K geometry
%K wave function
%K structure
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]Preprints, Working Papers, ...
%X 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 $b$. For $b\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $b$ and $1/b$. 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 DT 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.
%G English
%L hal-04344232
%U https://hal.science/hal-04344232
%~ CNRS
%~ LPTHE
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ SU-SCIENCES
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021