Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings

By Marcos Mariño, R. Schiappa, Marlene Weiss. 2007

181 citations recorded by the source corpus.

This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining explicit results for the one-instanton amplitude at both one and two loops. The holographic description of topological strings in terms of matrix models implies that our nonperturbative results also apply to topological strings on toric Calabi-Yau manifolds. This yields very precise predictions for the large-order behavior of the perturbative genus expansion, both in conventional matrix models and in topological string theory. We test these predictions in detail in various examples, including the quartic matrix model, topological strings on the local curve, and Hurwitz theory. In all these cases we provide extensive numerical checks which heavily support our nonperturbative analytical results. Moreover, since all these models have a critical point describing two-dimensional gravity, we also obtain in this way the large-order asymptotics of the relevant solution to the Painleve I equation, including corrections in inverse genus. From a mathematical point of view, our results predict the large-genus asymptotics of simple Hurwitz numbers and of local Gromov-Witten invariants.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e567084a407b329e0dd981ae32a1460f426f5378

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Stanford
2. S. Shenker
3. Marcos Mariño
4. Phil Saad
5. M. Unsal
6. R. Schiappa
7. Daniele Dorigoni
8. Pavel Putrov

In Nuclear and High Energy Physics

1. Marcos Mariño
2. M. Unsal
3. Phil Saad
4. D. Stanford
5. G. Dunne
6. S. Shenker
7. J. Maldacena
8. Daniele Dorigoni

In Statistical and Nonlinear Physics

1. Phil Saad
2. Marcos Mariño
3. D. Stanford
4. S. Shenker
5. Pavel Putrov
6. M. Unsal
7. N. Drukker
8. Daniele Dorigoni

Citations in the corpus

• JT gravity as a matrix integral (2019, methodology): “In this section we will use the density of eigenvalues in the forbidden region to predict the large genus asymptotics of the Weil-Petersson volumes, following a similar approach for other problems described by topological recursion in [111, 112, 61].”
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, methodology): “Both [11] and [16] are based on the geometric description of the 1/N expansion in terms of a spectral curve.”
• 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”
• An introduction to resurgence, trans-series and alien calculus (2014, background): “Similarly in quantum mechanics [3–5], matrix models [6, 7] and topological strings [8], we encounter the same factorial growth of the coefficients cn in (1.”
• The Resurgence of Instantons in String Theory (2011, methodology): “, [15, 12, 42, 13] for discussions in the context of matrix models, and topological and minimal strings) F (z) ' z−nβ e−nAz +∞ ∑”
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, methodology): “We note that similar expressions have appeared in the context of matrix models and topological string theory [38, 67] and by using the bridge equations in the context of resurgence theory in [39].”
• From Weak to Strong Coupling in ABJM Theory (2010, background): “2 of [64] for more details on the large”
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “3.1 The Gaussian Matrix Model 18 3.2 The Penner Matrix Model 20 3.3 The Chern–Simons Matrix Model 21 3.4 Double–Scaling Limit and c = 1 Behavior 25”
• Nonperturbative aspects of ABJM theory (2011, methodology): “3) is just the leading behavior of the full asymptotics at large g, which involves a series of corrections in 1/g (see for example [15] for more details).”
• 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].”