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Quantum curve for strip geometries, topological recursion and open GW/DT invariants
Sibasish Banerjee1, Alexander Hock2
1Institut des Hautes Études Scientifiques (IHES), 35 Route de Chartres, 91440 Bures-sur-Yvette, France.
Abstract:
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.
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