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Masahide Manabe

Publications and source records attributed to Masahide Manabe.

At least 19 recordsLinked to original sources
arXiv2025

A Hamiltonian Formalism for Topological Recursion

We propose a string field Hamiltonian formalism that associates a class of spectral curves and provides their quantization through the Chekhov-Eynard-Orantin topological recursion. As illustrative examples, we present Hamiltonians for the $(2,2m-1)$ minimal discrete and continuum dynamical triangulation (DT) models, the supersymmetric analogue of minimal continuum DT models, the Penner model, and 4D $\mathcal{N}=2$ $SU(2)$ gauge theories in the self-dual $\Omega$-background.

math-ph↗
arXiv2025

Multicritical Dynamical Triangulations and Topological Recursion

We explore a continuum theory of multicritical dynamical triangulations and causal dynamical triangulations in two-dimensional quantum gravity from the perspective of the Chekhov-Eynard-Orantin topological recursion. The former model lacks a causal time direction and is governed by the two-reduced $W^{(3)}$ algebra, whereas the latter model possesses a causal time direction and is governed by the full $W^{(3)}$ algebra. We show that the topological recursion solves the Schwinger-Dyson equations for both models, and we explicitly compute several amplitudes.

hep-th↗
arXiv2025

Dynamical Triangulations for 2D Pure Gravity and Topological Recursion

We show that, in two-dimensional Euclidean quantum gravity without matter fields, the Schwinger-Dyson equations derived within the Hamiltonian framework of non-critical string field theory can be reformulated in terms of the Chekhov-Eynard-Orantin topological recursion, and we explicitly compute the associated low-order amplitudes. In particular, we establish this reformulation for two discrete models -- the basic type and the strip type -- as well as for the continuum limit of dynamical triangulations.

hep-th↗
arXiv2023

Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions

Via Andersen-Borot-Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur-Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's recursion based on physical two-dimensional gravity models related to the Jackiw-Teitelboim gravity and to provide an introduction to various realizations of topological recursion. For generalized Mirzakhani's recursions involving a Masur-Veech type twist, we derive Virasoro constraints and cut-and-join equations, and also show some computations of generalized volumes for the physical two-dimensional gravity models.

math-ph↗
arXiv2021

The colored Jones polynomials as vortex partition functions

We construct 3D $\mathcal{N}=2$ abelian gauge theories on $\mathbb{S}^2 \times \mathbb{S}^1$ labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones polynomials of knots in $\mathbb{S}^3$. The colored Jones polynomials are obtained as the Wilson loop expectation values along knots in $SU(2)$ Chern-Simons gauge theories on $\mathbb{S}^3$, and then our construction provides an explicit correspondence between 3D $\mathcal{N}=2$ abelian gauge theories and 3D $SU(2)$ Chern-Simons gauge theories. We verify, in particular, the applicability of our constructions to a class of tangle diagrams of 2-bridge knots with certain specific twists.

hep-th↗
arXiv2020

$\widehat{\mathfrak{sl}}(n)_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb {C}}^2/{\mathbb {Z}}_n$

Generalizations of the AGT correspondence between 4D $\mathcal{N}=2$ $SU(2)$ supersymmetric gauge theory on ${\mathbb {C}}^2$ with $Ω$-deformation and 2D Liouville conformal field theory include a correspondence between 4D $\mathcal{N}=2$ $SU(N)$ supersymmetric gauge theories, $N = 2, 3, \ldots$, on ${\mathbb {C}}^2/{\mathbb {Z}}_n$, $n = 2, 3, \ldots$, with $Ω$-deformation and 2D conformal field theories with $\mathcal{W}^{\, para}_{N, n}$ ($n$-th parafermion $\mathcal{W}_N$) symmetry and $\widehat{\mathfrak{sl}}(n)_N$ symmetry. In this work, we trivialize the factor with $\mathcal{W}^{\, para}_{N, n}$ symmetry in the 4D $SU(N)$ instanton partition functions on ${\mathbb {C}}^2/{\mathbb {Z}}_n$ (by using specific choices of parameters and imposing specific conditions on the $N$-tuples of Young diagrams that label the states), and extract the 2D $\widehat{\mathfrak{sl}}(n)_N$ WZW conformal blocks, $n = 2, 3, \ldots$, $N = 1, 2, \ldots\, .$

hep-th↗
arXiv2019

Reconstructing GKZ via topological recursion

In this article, a novel description of the hypergeometric differential equation found from Gel'fand-Kapranov-Zelevinsky's system (referred to GKZ equation) for Givental's $J$-function in the Gromov-Witten theory will be proposed. The GKZ equation involves a parameter $\hbar$, and we will reconstruct it as the WKB expansion from the classical limit $\hbar\to 0$ via the topological recursion. In this analysis, the spectral curve (referred to GKZ curve) plays a central role, and it can be defined as the critical point set of the mirror Landau-Ginzburg potential. Our novel description is derived via the duality relations of the string theories, and various physical interpretations suggest that the GKZ equation is identified with the quantum curve for the brane partition function in the cohomological limit. As an application of our novel picture for the GKZ equation, we will discuss the Stokes matrix for the equivariant $\mathbb{C}\textbf{P}^{1}$ model and the wall-crossing formula for the total Stokes matrix will be examined. And as a byproduct of this analysis we will study Dubrovin's conjecture for this equivariant model.

math-ph↗
arXiv2019

Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence

In [1, 2], Nekrasov applied the Bethe/gauge correspondence to derive the $\mathfrak{su}\, (2)$ XXX spin-chain coordinate Bethe wavefunction from the IR limit of a 2D $\mathcal{N}=(2, 2)$ supersymmetric $A_1$ quiver gauge theory with an orbifold-type codimension-2 defect. Later, Bullimore, Kim and Lukowski implemented Nekrasov's construction at the level of the UV $A_1$ quiver gauge theory, recovered his result, and obtained further extensions of the Bethe/gauge correspondence [3]. In this work, we extend the construction of the defect to $A_M$ quiver gauge theories to obtain the $\mathfrak{su} \, ( M + 1 )$ XXX spin-chain nested coordinate Bethe wavefunctions. The extension to XXZ spin-chain is straightforward. Further, we apply a Higgsing procedure to obtain more general $A_M$ quivers and the corresponding wavefunctions, and interpret this procedure (and the Hanany-Witten moves that it involves) on the spin-chain side in terms of Izergin-Korepin-type specializations (and re-assignments) of the parameters of the coordinate Bethe wavefunctions.

hep-th↗
arXiv2018

Macdonald topological vertices and brane condensates

We show, in a number of simple examples, that Macdonald-type $qt$-deformations of topological string partition functions are equivalent to topological string partition functions that are without $qt$-deformations but with brane condensates, and that these brane condensates lead to geometric transitions.

hep-th↗
arXiv2018

Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions

We examine a class of Calabi-Yau varieties of the determinantal type in Grassmannians and clarify what kind of examples can be constructed explicitly. We also demonstrate how to compute their genus-0 Gromov-Witten invariants from the analysis of the Givental $I$-functions. By constructing $I$-functions from the supersymmetric localization formula for the two dimensional gauged linear sigma models, we describe an algorithm to evaluate the genus-0 A-model correlation functions appropriately. We also check that our results for the Gromov-Witten invariants are consistent with previous results for known examples included in our construction.

hep-th↗
arXiv2018

Local B-model Yukawa couplings from A-twisted correlators

Using the exact formula for the A-twisted correlation functions of the two dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model, we reconsider the computation of the B-model Yukawa couplings of the local toric Calabi-Yau varieties. Our analysis is based on an exact result that has been evaluated from the supersymmetric localization technique and careful treatment of its application. We provide a detailed description of a procedure to investigate the local B-model Yukawa couplings and also test our prescription by comparing the results with known expressions evaluated from the local mirror symmetry approach. In particular, we find that the ambiguities of classical intersection numbers of a certain class of local toric Calabi-Yau varieties discovered previously can be interpreted as degrees of freedom of the twisted mass deformations.

hep-th↗
arXiv2017

From CFT to Ramond super-quantum curves

As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular vectors of a certain (e.g. Virasoro or super-Virasoro) underlying algebra. In this paper we reformulate this problem in the language of conformal field theory. Such a reformulation has several advantages: it leads to the identification of quantum curves more efficiently, it proves in full generality that they indeed have the structure of singular vectors, it enables identification of corresponding eigenvalue models. Moreover, this approach can be easily generalized to other underlying algebras. To illustrate these statements we apply the conformal field theory formalism to the case of the Ramond version of the super-Virasoro algebra. We derive two classes of corresponding Ramond super-eigenvalue models, construct Ramond super-quantum curves that have the structure of relevant singular vectors, and identify underlying Ramond super-spectral curves. We also analyze Ramond multi-Penner models and show that they lead to supersymmetric generalizations of BPZ equations.

hep-th↗
arXiv2017

Singular vector structure of quantum curves

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.

hep-th↗
arXiv2017

Quantum curves and conformal field theory

To a given algebraic curve we assign an infinite family of quantum curves (Schrödinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model we build such quantum curves out of an appropriate representation of the Virasoro algebra, encoded in the structure of the $α/β$-deformed matrix integral and its loop equation. We generalize this construction to a large class of algebraic curves by means of a refined topological recursion. We also specialize this construction to various specific matrix models with polynomial and logarithmic potentials, and among other results, show that various ingredients familiar in the study of conformal field theory (Ward identities, correlation functions and a representation of Virasoro operators acting thereon, BPZ equations) arise upon specialization of our formalism to the multi-Penner matrix model.

hep-th↗
arXiv2017

Enumeration of chord diagrams via topological recursion and quantum curve techniques

In this paper we consider the enumeration of orientable and non-orientable chord diagrams. We show that this enumeration is encoded in appropriate expectation values of the $β$-deformed Gaussian and RNA matrix models. We evaluate these expectation values by means of the $β$-deformed topological recursion, and - independently - using properties of quantum curves. We show that both these methods provide efficient and systematic algorithms for counting of chord diagrams with a given genus, number of backbones and number of chords.

math-ph↗
arXiv2017

Partial chord diagrams and matrix models

In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.

math-ph↗
arXiv2016

Super-quantum curves from super-eigenvalue models

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce $β$-deformed version of those models, and derive differential equations for associated $α/β$-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

hep-th↗