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<p>Open topological string partition function gives rise to open Gromov–Witten invariants, open Donaldson–Thomas invariants and 3D-5D BPS indices. Utilizing the remodeling conjecture which connects topological recursion and topological string theory, in this paper we study open topological string theory for the subclass of toric Calabi–Yau threefold known as strip geometries. For this purpose, certain new developments in the theory of topological recursion are applied as its extension to logarithmic topological recursion (Log-TR) and the universal <i>x</i>–<i>y</i> duality. Through this, we derive the open topological string partition function and also the associated quantum curve. We also explain how this is related to the open Donaldson–Thomas partition function associated with certain symmetric quivers, exponential networks and <i>q</i>-Barnes-type integrals. In the process, we also connect how 3D-5D wall-crossing affects these partition functions as one varies <i>x</i>, in examples.</p>

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Quantum curve for strip geometries, topological recursion and open GW/DT invariants

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Sibasish Banerjee,
  • Alexander Hock

摘要

Open topological string partition function gives rise to open Gromov–Witten invariants, open Donaldson–Thomas invariants and 3D-5D BPS indices. Utilizing the remodeling conjecture which connects topological recursion and topological string theory, in this paper we study open topological string theory for the subclass of toric Calabi–Yau threefold known as strip geometries. For this purpose, certain new developments in the theory of topological recursion are applied as its extension to logarithmic topological recursion (Log-TR) and the universal x–y duality. Through this, we derive the open topological string partition function and also the associated quantum curve. We also explain how this is related to the open Donaldson–Thomas partition function associated with certain symmetric quivers, exponential networks and q-Barnes-type integrals. In the process, we also connect how 3D-5D wall-crossing affects these partition functions as one varies x, in examples.