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Large N duality beyond the genus expansion

Marino, M, Pasquetti, S and Putrov, P (2009) Large N duality beyond the genus expansion J HIGH ENERGY PHYS.

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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.

Item Type: Article
Divisions : Surrey research (other units)
Authors :
Marino, M
Putrov, P
Date : 24 November 2009
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:30
Last Modified : 24 Jan 2020 22:23

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