Quantum geometry of refined topological strings

By Mina Aganagic, Miranda C. N. Cheng, R. Dijkgraaf, Daniel Krefl, C. Vafa. Journal of High Energy Physics, 2011

268 citations recorded by the source corpus.

We consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrödinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description. Furthermore, in the limit where one of the equivariant rotations approaches zero, the brane partition function satisfies a time-independent Schrödinger equation. We use this observation, as well as the back reaction of the brane on the closed string geometry, to offer an explanation of the connection between integrable systems and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=2 $\end{document} gauge systems in four dimensions observed by Nekrasov and Shatashvili.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/953716568372864d48843fae5de5a91fd248fd2f

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Citations in the corpus

ABJM theory as a Fermi gas (2011, methodology): “Our formalism has many similarities with recent developments matrix models and topological string theory (see, for some examples, [57, 58, 59]).”
Knot Homology from Refined Chern-Simons Theory (2011, background): “This results in two different kinds of branes of the refined topological string [64,22].”
Topological Strings from Quantum Mechanics (2014, methodology): “By using the quantum mirror map for local P1 × P1 [17], one has π~Ja(μ) = −4e−2μ+ ( −2q − 2 q − 14 ) e−4μ+ ( −4q(2) − 4 q2 − 24q − 24 q − 232 3 ) e−6μ+· · · , (5.”
Non-perturbative effects and the refined topological string (2013, methodology): “Note that the natural solution of the Schrödinger equation that we have presented here, following [19], is an expansion in z but exact in ~.”
The String Landscape, the Swampland, and the Missing Corner (2017, methodology): “Here we can clearly identify the pair of Seiberg-Witten data (ydx,Σ) = (λSW , ΣSW ) from first principles [132].”
Torus Knots and Mirror Symmetry (2011, background): “The topological recursion of [19], which computes open and closed topological string amplitudes in toric Calabi–Yau manifolds, might have a generalization which gives the mirror of the refined topological vertex [25] (recent work in this direction can be found in [1]).”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “This so-called Nekrasov-Shatashvili limit has subsequently been studied in a series of papers [23, 87, 88].”