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,L), and we test it numerically to high precision in order to exhibit the importance of instanton effects. © SISSA 2010

Mariño, M., Pasquetti, S., Putrov, P. (2010). Large at duality beyond the genus expansion. JOURNAL OF HIGH ENERGY PHYSICS, 2010(7) [10.1007/JHEP07(2010)074].

Large at duality beyond the genus expansion

PASQUETTI, SARA
Secondo
;
2010

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,L), and we test it numerically to high precision in order to exhibit the importance of instanton effects. © SISSA 2010
Articolo in rivista - Articolo scientifico
1/N expansion; Chern-simons theories; Gauge-gravity correspondence; Topological strings; Nuclear and High Energy Physics;
English
Mariño, M., Pasquetti, S., Putrov, P. (2010). Large at duality beyond the genus expansion. JOURNAL OF HIGH ENERGY PHYSICS, 2010(7) [10.1007/JHEP07(2010)074].
Mariño, M; Pasquetti, S; Putrov, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/145688
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