Riemann-Hilbert problems for the resolved conifold

Abstract

We study the Riemann-Hilbert problems associated to the Donaldson-Thomas theory of the resolved conifold. We give explicit solutions in terms of the Barnes double and triple sine functions. We show that the corresponding tau function is a non-perturbative partition function, in the sense that its asymptotic expansion coincides with the topological string partition function.

35 pages, 3 figures. This version corrects yet another sign error

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The quantum dilogarithm and representations quantum cluster varieties
• Three questions in Gromov-Witten theory
• Spaces of stability conditions
• Riemann-Hilbert problems from Donaldson-Thomas theory

Cited by in corpus (3)

• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• A Hyperkähler geometry associated to the BPS structure of the resolved conifold
• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies