Mathematical Structures of Non-perturbative Topological String Theory: From GW to DT Invariants

Abstract We study the Borel summation of Gromov–Witten potential for resolved conifold. The Stokes phenomena associated to this are shown encode Donaldson–Thomas (DT) invariants conifold, having a direct relation Riemann–Hilbert problem formulated by Bridgeland (Invent Math 216(1), 69–124, 2019). There exist distinguished integration contours which reproduces previous proposals non-perturbative topological string partition functions These have another asymptotic expansion at strong coupling. demonstrate that strong-coupling DT conifold in second way. Mathematically, one finds problems is different from found weak turn out be closely related wall-crossing spectrum BPS states on studied context supergravity Jafferis and Moore (Wall crossing local Calabi Yau manifolds, arXiv:0810.4909 , 2008).