Reconstructing WKB from topological recursion

Bouchard, Vincent; Eynard, Bertrand

doi:10.5802/jep.58

Cited by 70 publications

(188 citation statements)

References 90 publications

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“…and then we find 47) for momenta α = ±β ±1/2 . This quantum curve reduces to the supersymmetric algebraic curve, which can be written as…”

Section: Double Quantum Structurementioning

confidence: 61%

Singular vector structure of quantum curves

Ciosmak¹,

Hadasz²,

Manabe³

et al. 2018

Proceedings of Symposia in Pure Mathematics

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We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the super-eigenvalue model with the underlying super-Virasoro algebra. In the Virasoro case we relate singular vector structure of quantum curves to the topological recursion, and in the super-Virasoro case we introduce the notion of super-quantum curves. We also discuss the double quantum structure of the quantum curves and analyze specific examples of Gaussian and multi-Penner models.

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“…and then we find 47) for momenta α = ±β ±1/2 . This quantum curve reduces to the supersymmetric algebraic curve, which can be written as…”

Section: Double Quantum Structurementioning

confidence: 61%

Singular vector structure of quantum curves

Ciosmak¹,

Hadasz²,

Manabe³

et al. 2018

Proceedings of Symposia in Pure Mathematics

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show abstract

“…However, as is mentioned in [BCD] and [IS], quantum curves for higher genus (or non-admissible) spectral curves may include infinitely many -correction terms. It is also noticed that the admissible spectral curves in the sense of [BE2] must be of genus 0. Therefore, we cannot expect that there is a straightforward generalization of our results for those spectral curves.…”

Section: Resultsmentioning

confidence: 99%

Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion: Part II: For confluent family of hypergeometric equations

Iwaki

Koike

Takei

2019

Journal of Integrable Systems

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We show that the each member of the confluent family of the Gauss hypergeometric equations is realized as quantum curves for appropriate spectral curves. As an application, relations between the Voros coefficients of those equations and the free energy of their classical limit computed by the topological recursion are established. We will also find explicit expressions of the free energy and the Voros coefficients in terms of the Bernoulli numbers and Bernoulli polynomials.

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“…(C.12) can be thought of as the "quantum spectral curve" for the JT gravity. It would be interesting to study the property of (C.12) along the lines of [61,62]. Let us consider the string equation (C.10) for the JT gravity case.…”

Section: (C2)mentioning

confidence: 99%

JT gravity, KdV equations and macroscopic loop operators

Okuyama

Sakai

2020

J. High Energ. Phys.

222

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We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS 2 background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.

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Reconstructing WKB from topological recursion

Cited by 70 publications

References 90 publications

Singular vector structure of quantum curves

Singular vector structure of quantum curves

Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion: Part II: For confluent family of hypergeometric equations

JT gravity, KdV equations and macroscopic loop operators

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