Open string amplitudes and large order behavior in topological string theory

By Marcos Mariño. 2006

248 citations recorded by the source corpus.

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in particular we write down the annulus amplitude in terms of theta functions on a Riemann surface. We test these ideas on local curves and local surfaces, providing in this way generating functionals for open Gromov-Witten invariants in the spirit of mirror symmetry. In the case of local curves, we study the open string sector near the critical point which leads to 2d gravity, and we show that toric D-branes become FZZT branes in a double-scaling limit. We use this connection to compute non-perturbative instanton effects due to D-branes that control the large order behavior of topological string theory on these backgrounds.

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

View Paper: https://www.semanticscholar.org/paper/ff807c367340bae0450239c147bd8f1c8a52f8b8

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Citations in the corpus

Hurwitz numbers, matrix models and enumerative geometry (2007, methodology): “Z dM e −NTr V ( M ) , where V (x) is a polynomial, or more generally a power series in x. The main goal of matrix model theory is to compute (3.1) as well as the connected correlation functions”
A primer on resurgent transseries and their asymptotics (2018, background): “, [136, 51, 215, 134, 113, 114] (see [119] for further earlier references), the modern (physical) version of resurgence theory has itself recently resurged in many areas, from quantum mechanics [8–10, 242–244, 157, 7, 156, 158, 101, 27, 15, 129, 102, 187, 126, 122, 127, 221, 107, 166, 213, 65, 28, 1”
The Resurgence of Instantons in String Theory (2011, background): “The present research program started in [10, 15], which proposed to generalize many of the nonperturbative results previously obtained within minimal strings to the realm of matrix models off–criticality and topological strings (intimately related via [3], as aforementioned).”
From Weak to Strong Coupling in ABJM Theory (2010, background): “1), or equivalently from the formalism of [59] (appropriately modified as in [60,61]).”
A& B model approaches to surface operators and Toda thoeries (2010, methodology): “On the B-model side we propose and check by explicit compuatations that the effects of multiple surface operator insertions can be calculated using the B-model topological recursion approach [14, 15, 16].”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “Moreover the improved understanding of the mirror geometry, their GKZ systems and the role of non-renormalizable deformations can be be useful to study open string amplitudes and Wilson line amplitudes for the geometry of the tensionless string, the [p, q]-strings or the geometries more formally ass”
Topological Strings from Quantum Mechanics (2014, background): “It turns out [31, 32] that all the perturbative information about the B-model topological string on X̂ is encoded in the equation WX(e , e) = 0, (2.”
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].”
Invariants of spectral curves and intersection theory of moduli spaces of complex curves (2011, background): “More generally, it was initially proposed by Mariño [21] and refined by Bouchard– Klemm–Mariño–Pasquetti (BKMP) [4], that if we choose the spectral curve to be the mirror curve of a toric Calabi–Yau 3–fold X, then the W (g) n ’s should be generating functions for the Gromov–Witten invariants of X,”
Remodeling the B-Model (2007, methodology): “Various nontrivial examples were tested in [40] successfully.”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, methodology): “The Hurwitz model that we have discussed can be generalized to a family of topological string theories on non-compact Calabi–Yau manifolds (the so-called “local curves”) where nonperturbative effects can be also computed by using matrix model techniques, see [93, 100, 95].”
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, methodology): “Of course, it would be even more interesting to find explicit difference equations for the topological string partition function on other Calabi–Yau targets, or to translate the matrix model results of [62, 9] in such a framework.”
Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, methodology): “In [44, 10], Bouchard, Klemm, Mariño and Pasquetti (i.”
Direct integration of the topological string (2007, background): “In view of the results of [45], this could lead to a powerful approach to compute open string amplitudes on toric Calabi–Yau manifolds.”
A-polynomial, B-model, and quantization (2011, methodology): “Generally, for curves of arbitrary genus, the Bergman kernel is given by a derivative of a logarithm of the theta function of odd characteristic θodd associated to the classical curve C [12, 13] B(p1, p2) = ∂p1∂p2 log θodd ( u(p1) − u(p2) ) ,”
Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants (2011, methodology): “Important examples of the Eynard-Orantin invariants, using different choices of (C, x, y), store intersection numbers over the moduli space of curves [5]; simple Hurwitz numbers [1, 3, 6]; a count of lattice points in the moduli space of curves [17]; and conjecturally local Gromov-Witten invariants ”
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models (2009, background): “In particular, this implies that in this limit also the instanton action reduces to the c = 1 one which indicates, as also observed in [10], that in the double–scaling limit nonperturbative effects due to toric branes reduce to the ones due to Liouville branes in minimal models.”