Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants

2025/10/08 by Sibasish Banerjee, Alexander Hock, Banerjee, Sibasish +1 · 1 citation
Mathematics · #05A15 #14H81 #30F30 #81T30 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2510.07146

openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/31

Abstract

Open topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling 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.

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Cited by

• Skein-valued mirror curves for toric CY3 strips
• GW/DT invariants and 5D BPS indices for strips from topological recursion

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• From quantum curves to topological string partition functions II
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• Topological Strings and Quantum Curves