Abstract
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extended to refined Chern-Simons with orthogonal groups.
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Krefl, D., Mkrtchyan, R.L. Exact Chern-Simons / Topological String duality. J. High Energ. Phys. 2015, 45 (2015). https://doi.org/10.1007/JHEP10(2015)045
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DOI: https://doi.org/10.1007/JHEP10(2015)045