Abstract
We study non-perturbative aspects of the large N duality between Chern-Simons theory and topological strings, and we find a rich structure of large N phase transitions in the complex plane of the 't Hooft parameter. These transitions are due to large N instanton effects, and they can be regarded as a deformation of the Stokes phenomenon. Moreover, we show that, for generic values of the 't Hooft coupling, instanton effects are not exponentially suppressed at large N and they correct the genus expansion. This phenomenon was first discovered in the context of matrix models, and we interpret it as a generalization of the oscillatory asymptotics along anti-Stokes lines. In the string dual, the instanton effects can be interpreted as corrections to the saddle string geometry due to discretized neighbouring geometries. As a mathematical application, we obtain the 1/N asymptotics of the partition function of Chern-Simons theory on the lens space L(2, 1), and we test it numerically to high precision in order to exhibit the importance of instanton effects.
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ArXiv ePrint: arXiv:0911.4692
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Mariño, M., Pasquetti, S. & Putrov, P. Large N duality beyond the genus expansion. J. High Energ. Phys. 2010, 74 (2010). https://doi.org/10.1007/JHEP07(2010)074
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DOI: https://doi.org/10.1007/JHEP07(2010)074