We address the nonperturbative structure of topological strings and c = 1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern-Simons matrix models, together with their holographic duals, the c = 1 minimal string at self-dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all-loop multi-instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large-order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi-sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonperturbative ambiguity. Our predictions for the multi-instanton expansions are confirmed within the trans-series set-up, which in the double-scaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric D-brane instantons which, in the double-scaling limit, precisely match D-instanton contributions to c = 1 minimal strings. © 2010 Springer Basel AG

Pasquetti, S., Schiappa, R. (2010). Borel and stokes nonperturbative phenomena in topological string theory and c = 1 matrix models. ANNALES HENRI POINCARE', 11(3), 351-431 [10.1007/s00023-010-0044-5].

Borel and stokes nonperturbative phenomena in topological string theory and c = 1 matrix models

PASQUETTI, SARA
;
2010

Abstract

We address the nonperturbative structure of topological strings and c = 1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern-Simons matrix models, together with their holographic duals, the c = 1 minimal string at self-dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all-loop multi-instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large-order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi-sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonperturbative ambiguity. Our predictions for the multi-instanton expansions are confirmed within the trans-series set-up, which in the double-scaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric D-brane instantons which, in the double-scaling limit, precisely match D-instanton contributions to c = 1 minimal strings. © 2010 Springer Basel AG
Articolo in rivista - Articolo scientifico
Statistical and Nonlinear Physics; Nuclear and High Energy Physics; Mathematical Physics
English
351
431
81
Pasquetti, S., Schiappa, R. (2010). Borel and stokes nonperturbative phenomena in topological string theory and c = 1 matrix models. ANNALES HENRI POINCARE', 11(3), 351-431 [10.1007/s00023-010-0044-5].
Pasquetti, S; Schiappa, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/145693
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