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Kento Osuga

Publications and source records attributed to Kento Osuga.

18 recordsLinked to original sources
arXiv2026

Refined lattice point counting on the moduli space of Klein surfaces

We introduce the moduli space of metric M\"obius graphs, which extend ribbon graphs to the non-orientable world. This space contains both the moduli space of Riemann surfaces and the moduli space of non-orientable Klein surfaces. Each metric M\"obius graph is equipped with a measure of non-orientability. We count lattice points in this moduli space, weighted by the measure of non-orientability, and prove a refined version of Norbury's recursion for this count. Taking the limit as the mesh becomes finer, we deduce a recursion for the Euclidean volumes, yielding a refined version of the Witten--Kontsevich recursion. As an application, we give a geometric definition of the refined Euler characteristic of the moduli space and compute it explicitly, thereby answering a question of Goulden, Harer, and Jackson.

math.AG↗
arXiv2025

Volumes of moduli spaces of bordered Klein surfaces

We investigate volumes of moduli spaces of bordered Klein surfaces, which include non-orientable surfaces. On these moduli spaces, the top form introduced by Norbury diverges as the lengths of 1-sided geodesics approach zero. However, when integrated over Gendulphe's regularised moduli space, on which the systole of 1-sided geodesics is bounded below by $\epsilon\in\mathbb{R}_{>0}$, it returns a finite value. We derive an explicit formula for the volume of the moduli space of two-bordered real projective planes and of one-bordered Klein bottles --- the latter utilises Norbury's extension of the Mirzakhani--McShane identities to non-orientable surfaces. We then relate these results to refined topological recursion, showing that, for a fixed refinement parameter, the volumes of moduli spaces of Klein surfaces with Euler characteristic $-1$ are governed by this procedure. For general topologies, both approaches remain incomplete due to several difficulties, which we discuss in this work. Together with our results, this initiates the search for a geometric recursive structure governing the volumes of moduli spaces of bordered Klein surfaces, whose natural formulation may lie within a suitably extended version of refined topological recursion.

math.GT↗
arXiv2025

Superconformal topological recursion

We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric counterpart is what we call superconformal topological recursion defined on a super Riemann surface. Superconformal topological recursion indicates that odd holomorphic one-forms on a super Riemann surface are related to zero modes of copies of the Clifford algebras, and it also provides a tool to study deformation of non-split super Riemann surfaces, e.g. certain families of super Riemann surfaces carrying odd parameters. On a super Riemann surface over a non-reduced base, the formalism is recursive not only in terms of pants-decomposition but also in terms of odd parameters in a suitable sense.

math-ph↗
arXiv2024

$\mathfrak{b}$-Hurwitz numbers from refined topological recursion

We prove that single $G$-weighted $\mathfrak{b}$-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights $G$. Consequently, the $\mathfrak{b}$-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of $\mathfrak{b}$-monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre $\beta$-ensembles are computed by refined topological recursion.

math.CO↗
arXiv2024

$b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras

We show that $b$-Hurwitz numbers with a rational weight are obtained by taking an explicit limit of a Whittaker vector for the $\mathcal{W}$-algebra of type $A$. Our result is a vast generalization of several previous results that treated the monotone case, and the cases of quadratic and cubic polynomial weights. It also provides an interpretation of the associated Whittaker vector in terms of generalized branched coverings that might be of independent interest. Our result is new even in the special case $b=0$ that corresponds to classical hypergeometric Hurwitz numbers, and implies that they are governed by the topological recursion of Eynard-Orantin. This gives an independent proof of the recent result of Bychkov-Dunin-Barkowski-Kazarian-Shadrin.

math.AG↗
arXiv2023

Refined BPS structures and topological recursion - the Weber and Whittaker curves

We study properties of the recently established refined topological recursion for some simple spectral curves associated to quadratic differentials. We prove explicit formulas for the free energy and Voros coefficients of the corresponding quantum curves, and conjecture expressions for all other (smooth) genus zero degree two curves. The results can be written in terms of Bridgeland's notion of refined BPS structure associated to the same initial data, together with a quantum correction to the central charge. The corresponding "invariants" appear to be new, but their interpretation in terms of Donaldson-Thomas theory or QFT is not entirely clear.

math.AG↗
arXiv2023

Deformation and quantisation condition of the $\mathscr{Q}$-top recursion

We consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the $\mathscr{Q}$-top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the $\mathscr{Q}$-top recursion on a degenerate elliptic curve. We also discuss a relation to the corresponding Nekrasov-Shatashivili effective twisted superpotential.

math-ph↗
arXiv2023

Refined topological recursion revisited -- properties and conjectures

For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by Kidwai and the author, and also improving the proposal by Chekhov and Eynard. Along the way, we uncover a fundamental geometric structure underlying the hyperelliptic refined topological recursion and investigate its properties -- parts of which remain conjectural due to computational difficulties. Moreover, we establish a new recursion valid in the so-called Nekrasov-Shatashivili limit and prove existence of the corresponding quantum curve.

math-ph↗
arXiv2022

Quantum curves from refined topological recursion: the genus 0 case

We formulate geometrically (without reference to physical models) a refined topological recursion applicable to genus zero curves of degree two, inspired by Chekhov-Eynard and Marchal, introducing new degrees of freedom in the process. For such curves, we prove the fundamental properties of the recursion analogous to the unrefined case. We show the quantization of spectral curves due to Iwaki-Koike-Takei can be generalized to this setting and give the explicit formula, which turns out to be related to the unrefined case by a simple transformation. For an important collection of examples, we write down the quantum curves and find that in the Nekrasov-Shatashvili limit, they take an especially simple form.

math.AG↗
arXiv2021

Five-dimensional gauge theories and the local B-model

We propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi--Yau geometries related to the circle compactification of five-dimensional $\mathcal{N}=1$ super Yang--Mills theory with simple gauge group. In the simply-laced case, we construct Picard--Fuchs operators from the Dubrovin connection on the Frobenius manifolds associated to the extended affine Weyl groups of type $\mathrm{ADE}$. In general, we propose a purely algebraic construction of Picard--Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg--Witten curve, encompassing non-simply-laced cases as well. We offer several precision tests of our proposal. Whenever a candidate spectral curve is known from string theory/brane engineering, we perform non-perturbative comparisons with the gauge theory prepotentials obtained from the K-theoretic blow-up equations, finding perfect agreement. We also employ our formalism to rule out some proposals from the theory of integrable systems of Seiberg--Witten geometries for non-simply laced gauge groups.

hep-th↗
arXiv2021

Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks

We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $\mu$-twisted super topological recursion, and construct a dual algebraic description in terms of super Airy structures. We then show that the partition function of an appropriate super Airy structure coincides with the Gaiotto vector for $\mathcal{N}=1$ superconformal blocks in the Neveu-Schwarz or Ramond sector. Equivalently, the Gaiotto vector can be computed by the untwisted or $\mu$-twisted super topological recursion. This implies that the framework of the super topological recursion -- equivalently super Airy structures -- can be applied to compute the Nekrasov partition function of $\mathcal{N}=2$ pure $U(2)$ supersymmetric gauge theory on $\mathbb{C}^2/\mathbb{Z}_2$ via a conjectural extension of the Alday-Gaiotto-Tachikawa correspondence.

math-ph↗
arXiv2020

$\mathcal{N}=1$ Super Topological Recursion

We introduce the notion of $\mathcal{N}=1$ abstract super loop equations, and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the Eynard-Orantin topological recursion, based on the geometry of a local super spectral curve. The second approach is based on the framework of super Airy structures. The resulting recursive formalism can be applied to compute correlation functions for a variety of examples related to 2d supergarvity.

math-ph↗
arXiv2019

Topological Recursion in The Ramond Sector

We investigate supereigenvalue models in the Ramond sector and their recursive structure. We prove that the free energy truncates at quadratic order in Grassmann coupling constants, and consider super loop equations of the models with the assumption that the 1/N expansion makes sense. Subject to this assumption, we obtain the associated genus-zero algebraic curve with two ramification points (one regular and the other irregular) and also the supersymmetric partner polynomial equation. Starting with these polynomial equations, we present a recursive formalism that computes all the correlation functions of these models. Somewhat surprisingly, correlation functions obtained from the new recursion formalism have no poles at the irregular ramification point due to a supersymmetric correction -- the new recursion may lead us to a further development of supersymmetric generalizations of the Eynard-Orantin topological recursion.

hep-th↗
arXiv2019

Super Quantum Airy Structures

We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional -- which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss -- as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

math-ph↗
arXiv2019

Harmony for 2-Qubit Entanglement

In this Letter we present a new quantity that shows whether two general qubit systems are entangled, which we call harmony. It captures the notion of separability and maximal entanglement. It is also shown that harmony is monogamous for 3-qubit states. Thus, harmony serves as a new entanglement measure. In addition, since it is written as a simple function of the density operator, it is in practice easier to compute than other previously known measures.

quant-ph↗
arXiv2016

Qubit Transport Model for Unitary Black Hole Evaporation without Firewalls

We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.

hep-th↗
arXiv2016

A New Way to Derive the Taub-NUT Metric with Positive Cosmological Constant

We investigate a biaxial Bianchi IX model with positive cosmological constant, which is sometimes called the Lambda-Taub-NUT spacetime, whose exact solution is well known. The minisuperspace of biaxial Bianchi IX models admits two non-trivial Killing tensors that play an important role for deriving the Taub-NUT metric. We also give a brief discussion about the asymptotic behaviour of Bianchi IX models.

gr-qc↗