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**1 - 2**of**2**### Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models

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### Topological String Theory and c = 1 Matrix Models

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"... Abstract: We address the nonperturbative structure of topological strings and c = 1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large–order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern–Simons mat ..."

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Abstract: We address the nonperturbative structure of topological strings and c = 1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large–order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern–Simons matrix models, together with their holographic duals, the c = 1 minimal string at self–dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all–loop multi–instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large–order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi–sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonperturbative ambiguity. Our predictions for the multi–instanton expansions are confirmed within the trans– series set–up, which in the double–scaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric D–brane instantons which, in the double–scaling limit, precisely match D–instanton