Large N duality beyond the genus expansion

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 neighboring geometries. As a mathematical application, we obtain the 1/N asymptotics of the partition function of Chern-Simons theory on L(2,1), and we test it numerically to high precision in order to exhibit the importance of instanton effects.

37 pages, 24 figures. v2: clarifications and references added, misprints corrected, to appear in JHEP

References in corpus (5)

• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Open string amplitudes and large order behavior in topological string theory
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence
• Topological Strings and (Almost) Modular Forms

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