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Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions
Journal of Differential Geometry  (IF2.688),  Pub Date : 2020-07-09, DOI: 10.4310/jdg/1594260015
Tom Bridgeland

We study the Riemann-Hilbert problems of [6] (T. Bridgeland, “Riemann-Hilbert problems from Donaldson–Thomas theory”, arxiv:1611.03697) in the case of 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 $\tau$-function of [6] is a non-perturbative partition function, in the sense that its asymptotic expansion coincides with the topological closed string partition function.