Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models
By Sara Pasquetti, R. Schiappa. 2009
161 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/8c0be8df1290fc6ddb1ee1693d6c30fee4c253b3
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Citations in the corpus
- Analytic continuation of Liouville theory (2011, methodology): “(For a previous analysis along similar lines to what we will explain, see [12].”
- The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, background): “ and string theory, however, is quite recent. A few interesting works have appeared recently, predominantly in the context of matrix models and minimal strings by Marino,~ Schiappa, and collaborators [38,39,63]. All these works address theories without renormalons. In the context of asymptotically f”
- The Resurgence of Instantons in String Theory (2011, methodology): “This is also in line with the general expectations briefly discussed in [24].”
- From Weak to Strong Coupling in ABJM Theory (2010, unknown): “31) is similar to the one found for Chern–Simons theory on S3 in [65], and it should be governed by a large N instanton with action A(λ).”
- Nonperturbative aspects of ABJM theory (2011, unknown): “It was found in [27], for example, that due to the multivaluedness of the effective potential, the instanton actions in the Chern–Simons matrix model are given by 2πi (t+ 2πin) , n ∈ Z.”
- Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “3.1 Perturbation theory on R2 and IR-renormalons 22”
- Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “31) have their counterparts in matrix models and topological string theory [40, 41] and 4d gauge theory compactified on R3 × S1 [17].”
- A primer on resurgent transseries and their asymptotics (2018, background): “Recent such examples include different string-theoretic scenarios, as are the cases of the first Painlevé equations describing 2d (super) gravity [130, 16, 210] and topological string theory [199, 77, 78, 76].”
- An introduction to resurgence, trans-series and alien calculus (2014, background): “ know that this is not the case: one can show, via a saddle-point method, that indeed the perturbative coecients grow at higher orders as c n ˘n!. Similarly in quantum mechanics [5{7], matrix models [8,9] and topological strings [10], we encounter the same factorial growth of the coecients c nin (1.”
- Resurgence theory, ghost-instantons, and analytic continuation of path integrals (2013, methodology): “We call the set of all saddles the generalized instanton sector, following the works in d = 0 dimensional matrix models [11–19].”