Calabi-Yau Research Papers - Academia.edu (original) (raw)

2025, Springer eBooks

We study two dimensional N = (2, 2) Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large N techniques. We demonstrate the viability of such constructions and motivate the study of anisotropic tensor models. Such theories are a novel deformation of tensor models where we break the continuous symmetries while preserving the large N solvability. Specifically, we examine theories with superpotentials involving tensor contractions chosen to pick out melonic diagrams. The anisotropy is introduced by further biasing individual terms by different coefficients, all of the same order, to retain large N scaling. We carry out a detailed analysis of the resulting low energy fixed point and comment on potential applications to holography. Along the way we also examine gauged versions of the models (with partial anisotropy) and find generically that such theories have a non-compact Higgs branch of vacua.

2025, Landon Dean Cherry

The study of open and closed string worldsheets is fundamental and foundational for understanding string behavior, boundary conditions, and action formalism in modern string theory. This review presents the topological and dynamical distinctions between open and closed string configurations, including their origins, momenta, and actions that dictate the string evolution and energy profile. Central to strings evolution and energy profile is the Polyakov action, the Polyakov action offers a more holistic view of how strings evolve and interact across their worldsheet.

2025, Double stochastic processes and Generalized Chapman- Kolmogorov equations.

In this paper generalized Chapman-Kolmogorov equation is derived. 1.Introduction 2.Generalized random variables. 3.Integration over random interval. 4.Generalized Chapman-Kolmogorov equation. .

2025, arXiv (Cornell University)

We consider the spectral problem on ∂Ω in a smooth bounded domain Ω of R 2 . The factor ρ ε which appears in the first equation plays the role of a mass density and it is equal to a constant of order ε -1 in an ε-neighborhood of the boundary and to a constant of order ε in the rest of Ω. We study the asymptotic behavior of the eigenvalues λ(ε) and the eigenfunctions u ε as ε tends to zero. We obtain explicit formulas for the first and second terms of the corresponding asymptotic expansions by exploiting the solutions of certain auxiliary boundary value problems.

2025, SIAM Journal on Mathematical Analysis

2025, Homology, Homotopy and Applications

We extend the Oprea's result G1(S 2n+1 /H) = ZH to the 1 st generalized Gottlieb group G f 1 (S 2n+1 /H) for a map f : A → S 2n+1 /H. Then, we compute or estimate the groups G f m (S 2n+1 /H) and P f m (S 2n+1 /H) for some m > 1 and... more

2025

We introduce the notion of a matron M = ⊕Mn,m whose sub-modules ⊕M n,1 and ⊕M 1,m are non-Σ operads. We construct a functor from PROP to matrons and its inverse, the universal enveloping functor. We define the free matron H∞, generated by a singleton in each bidegree (m, n) = (1, 1), and define an A∞-bialgebra as an algebra over H∞. We realize H∞ as the cellular chains of polytopes KKn,m, among which KK n,0 and KK 0,m are Stasheff associahedra.

2025, arXiv (Cornell University)

Using embedding of complex curves in the complex projective plane P 2 , we develop a non planar topological 3-vertex formalism for topological strings on the family of local Calabi-Yau threefolds ∞) . The base E (t,∞) stands for the degenerate elliptic curve with Kahler parameter t; but a large complex structure µ; i.e |µ| -→ ∞. We also give first results regarding A-model topological string amplitudes on X (m,-m,0) . The 2D U (1) gauged N = 2 supersymmetric sigma models of the degenerate elliptic curve E (t,∞) as well as for the family X (m,-m,0) are studied and the role of D-and F-terms is explicitly exhibited.

2025

It is shown how some field theories in the target-space induce the splitting of the space-time into a continuous of branes, which can be p-branes or D-branes depending on what the field theory it is. The basic symmetry underlying the construction is used to build an invariant action, which is proved to be off-shell identical to the p-brane (D-brane) action. The coupling with the abelian ($p+1$)-form in this formulation it is also found. While the classical brane's embedding couple to the field strenght, the classical fields couple with its dual (in the Hodge sense), therefore providing an explicit electric-magnetic duality. Finally, the generic role of the underlying symmetry in the connection between the target-space theory and the world-volume one, is completely elucidated.

2025, The journal of fourier analysis and applications/Journal of fourier analysis & applications

In this paper we use some ideas from and consider the description of Hörmander type pseudo-differential operators on R d (d ≥ 1), including the case of the magnetic pseudo-differential operators introduced in [15, 16], with respect to a tight Gabor frame. We show that all these operators can be identified with some infinitely dimensional matrices whose elements are strongly localized near the diagonal. Using this matrix representation, one can give short and elegant proofs to classical results like the Calderón-Vaillancourt theorem and Beals' commutator criterion, and also establish local trace-class criteria.

2025, American Mathematical Society eBooks

We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a two-dimensional Galois representation. By using the Lefschetz fixed-point theorem in étale cohomology and counting points on the variety over finite fields, this Galois representation is shown to be modular.

2025, Journal of Number Theory

BRUEN, JENSEN. AND YUI with certain Frobenius groups as Galois groups. 111.1. Preliminary results. 111.2. Realization of Frobenius groups of prime degree as Galois groups (general existence theorem). 111.3. Construction of polynomials with Galois group F,,, , bl over 0. 111.4. Construction of generic family of polynomials with Galois group F,c p I uz (p = 3 (mod 4)). 111.5. Special examples. 111.6. Remarks and problems. IV. Frobenius fields. IV.1. Frobenius fields over 0. IV.2. Frobenius fields over function fields.

2025, Expositiones Mathematicae

The proof of Serre's conjecture on Galois representations over finite fields allows us to show, using a trick due to Serre himself, that all rigid Calabi-Yau threefolds defined over Q are modular.

2025, International Journal of Robust and Nonlinear Control

In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. As a result of this process methane is produced. This model is known to be practically validated and reliable. Two feedback control laws are proposed (one of them is adaptive) for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. Computer simulations are reported to compare the effectiveness of the proposed feedbacks.

2025, Nuclear Physics B

We obtain a closed form expression for the Action describing pure gravity, in light-cone gauge, in a four-dimensional Anti de Sitter background. We perform a perturbative expansion of this closed form result to extract the cubic... more

2025, arXiv (Cornell University)

We introduce the notion of complex G 2 manifold M C , and complexification of a G 2 manifold M ⊂ M C . As an application we show the following: If (Y, s) is a closed oriented 3-manifold with a Spin c structure, and (Y, s) ⊂ (M, ϕ) is an imbedding as an associative submanifold of some G 2 manifold (such imbedding always exists), then the isotropic associative deformations of Y in the complexified G 2 manifold M C is given by Seiberg-Witten equations.

2025

Bosonization (and fermionization) in (1+1) dimensions is viewed as two dierent gauge xings of an underlying theory containing both types of elds.

2025, Communications in Mathematical Physics

We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U (N ). The model solves the general combinatorial problem of counting branched covers of orientable Riemann surfaces with any given, fixed branch point structure. We then define an appropriate continuum limit allowing the branch points to freely float over the surface. The simplest such limit reproduces two-dimensional chiral U (N ) Yang-Mills theory and its string description due to Gross and Taylor.

2025

La materia oscura, componente fundamental en el modelo cosmol´ogico est´andar,
carece de detecci´on directa y su naturaleza permanece desconocida. En este trabajo
se propone una hip´otesis alternativa basada en la teor´ ıa del tiempo como pulso
causal ontol´ogico. Se plantea que la materia oscura surge como una manifestaci´on
geom´etrica y din´amica de las modulaciones locales del pulso temporal fundamental,
que generan curvaturas espaciales adicionales sin necesidad de materia convencional.
Se formaliza esta idea y se discuten sus implicaciones y posibles v´ ıas experimentales.

2025, International Journal of Modern Physics

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyper-planar and the entire moduli space stabilities may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a non-interacting basis at the zeros of the scalar curvature, where the scalar fields become un-correlated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilizations of gauge and string moduli.

2025, Physical review

We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field in the region between two co-dimension one branes on the background of locally AdS spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to Aharonov-Bohm type effect on the vacuum currents. There exists a range in the space of the Robin coefficients for separate branes where the vacuum state becomes unstable. Compared to the case of the standard AdS bulk, in models with compact dimensions the stability condition imposed on the parameters is less restrictive. The current density has nonzero components along compact dimensions only. These components are decomposed into the brane-free and brane-induced contributions. Different representations are provided for the latter well suited for the investigation of the near-brane, near-AdS boundary and near-AdS horizon asymptotics. The component along a given compact dimension is a periodic function of the gauge field flux, enclosed by that dimension, with the period of the flux quantum. An important feature, that distinguishes the current density from the expectation values of the field squared and energy-momentum tensor, is its finiteness on the branes. In particular, for Dirichlet boundary condition the current density vanishes on the branes. We show that, depending on the constants in the boundary conditions, the presence of the branes may either increase or decrease the current density compared with that for the brane-free geometry. Applications are given to the Randall-Sundrum 2-brane model with extra compact dimensions. In particular, we estimate the effects of the hidden brane on the current density on the visible brane.

2025, Selecta Mathematica

The condition of having an N = 1 spacetime supersymmetry for heterotic string leads to 4 distinct possibilities for compactifications namely compactifications down to 6,4,3 and 2 dimensions. Compactifications to 6 and 4 dimensions have been studied extensively before (corresponding to K3 and a Calabi-Yau threefold respectively). Here we complete the study of the other two cases corresponding to compactification down to 3 on a 7 dimensional manifold of G 2 holonomy and compactification down to 2 on an 8 dimensional manifold of Spin( ) holonomy. We study the extended chiral algebra and find the space of exactly marginal deformations. It turns out that the role the U (1) current plays in the N = 2 superconformal theories, is played by tri-critical Ising model in the case of G 2 and Ising model in the case of Spin(7) manifolds. Certain generalizations of mirror symmetry are found for these two cases. We also discuss the topological twisting in each case.

2025, Journal of High Energy Physics

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The N = 1 superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE N = 2 superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single D3-brane and discuss the near-horizon supergravity solution for a large number N of coincident D3-branes.

2025, arXiv (Cornell University)

The Bagger-Witten line bundle is a line bundle over moduli spaces of two-dimensional SCFTs, related to the Hodge line bundle of holomorphic top-forms on Calabi-Yau manifolds. It has recently been a subject of a number of conjectures, but concrete examples have proven elusive. In this paper we collect several results on this structure, including a proposal for an intrisic geometric definition over moduli spaces of Calabi-Yau manifolds and some additional concrete examples. We also conjecture a new criterion for UV completion of four-dimensional supergravity theories in terms of properties of the Bagger-Witten line bundle.

2025, arXiv (Cornell University)

This is a summary of a talk given at the Vienna homological mirror symmetry conference in June 2006. We review how both derived categories and stacks enter physics. The physical realization of each has many formal similarities. For example, in both cases, equivalences are realized via renormalization group flow: in the case of derived categories, (boundary) renormalization group flow realizes the mathematical procedure of localization on quasiisomorphisms, and in the case of stacks, worldsheet renormalization group flow realizes presentation-independence. For both, we outline current technical issues and applications.

2025, arXiv (Cornell University)

In this paper we discuss noninvertible topological operators in the context of one-form symmetries and decomposition of two-dimensional quantum field theories, focusing on twodimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how bulk Wilson lines act as defects bridging universes, and how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries.

2025, arXiv (Cornell University)

In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather are literally sigma models on objects called quotient stacks, which are closely related to (but not quite the same as) quotient spaces. We show how this is an immediate consequence of definitions, and also how this explains a number of features of string orbifolds, from the fact that the CFT is well-behaved to orbifold Euler characteristics. Put another way, many features of string orbifolds previously considered "stringy" are now understood as coming from the target-space geometry; one merely needs to identify the correct target-space geometry.

2025, Advances in Theoretical and Mathematical Physics

In this paper, we shall describe some correlation function computations in perturbative heterotic strings that generalize B model computations. On the (2,2) locus, correlation functions in the B model receive no quantum corrections, but off the (2,2) locus, that can change. Classically, the (0,2) analogue of the B model is equivalent to the previously discussed (0,2) analogue of the A model, but with the gauge bundle dualizedour generalization of the A model also simultaneously generalizes the B model. The A and B analogues sometimes have different regularizations, however, which distinguish them quantum-mechanically. We discuss how properties of the (2,2) B model, such as the lack of quantum corrections, are realized in (0,2) A model language. In an appendix, we also extensively discuss how the Calabi-Yau condition for the closed string B model (uncoupled to topological gravity) can be weakened slightly, a detail which does not seem to have been covered in the literature previously. That weakening also manifests in the description of the (2,2) B model as a (0,2) A model.

2025

Dirichlet series, or, series of the form D(A, s) = ∞ i=1 a i i s are central objects in complex analysis and analytic number theory. This paper seeks to generalize them by introducing & studying new types of Dirichlet series-quaternionic Dirichlet series, and lattice Dirichlet series. That is, Dirichlet series over quaternions, and, various types of Dirichlet series over lattices.

2025, The Lazenby Twist Law: Memory Spectrum and Topological Dynamics

I introduce a novel topological invariant-the Memory Spectrum-emerging from the behavior of loops in structured 3D bubble spaces. I define memory cohomology classes, construct the Memory Laplacian ∆ m , and prove formal theorems capturing how memory propagates through topological environments. This theory has implications for quantum geometry, categorical topology, and new physical invariants.

2025

While exploring Dirichlet L-functions as part of a final-year project, I stumbled upon a surprising property: a wave function ψp(x) = χ(p)e iγx , where χ is a non-trivial Dirichlet character modulo q, γ is a non-trivial zero of L(s, χ), and p is a prime, produces a discrete Fourier transform ψp(k) with a dominant peak at k ≡ p -1 mod q. This "mirror symmetry" suggests a deep arithmetic structure linking primes to their modular inverses. I formalize this observation with a quantitative conjecture, provide numerical evidence for q = 5, 13, 17, and offer a partial theoretical analysis using Gauss and Kloosterman sums. Potential applications in quantum physics and cryptography are discussed. All data and code are available on Zenodo (DOI to be inserted).

2025, Physics Letters B

We show how an extremal Reissner-Nordström black hole can be obtained by wrapping a dyonic D3-brane on a Calabi-Yau manifold. In the orbifold limit T 6 /Z Z 3 , we explicitly show the correspondence between the solution of the... more

2025, arXiv (Cornell University)

A quaternionic version of the Calabi problem on the Monge-Ampère equation is introduced, namely a quaternionic Monge-Ampère equation on a compact hypercomplex manifold with an HKT-metric. The equation is non-linear elliptic of second order. For a hypercomplex manifold with holonomy in SL(n, H), uniqueness (up to a constant) of a solution is proven, as well as the zero order a priori estimate. The existence of a solution is conjectured, similar to the Calabi-Yau theorem. We reformulate this quaternionic equation as a special case of the complex Hessian equation, making sense on any complex manifold.

2025, Mayo

En este trabajo se analiza el esquema de compactificación y la estructura de modos de Fourier en una teoría unificada de 11 dimensiones basada en el formalismo de Kaluza-Klein. Se asocian 7 dimensiones compactas a 7 fuerzas gauge fundamentales, y se calcula el número aproximado de formas distintas de compactificar el espacio interno. Además, se desarrolla el análisis explícito de los modos de Fourier para campos gauge propagándose en dimensiones compactas tipo S 1 y (S 1) 7 .

2025

Cahiers de topologie et géométrie différentielle catégoriques, tome 29, n o 2 (1988), p. 87-108 <http © Andrée C. Ehresmann et les auteurs, 1988, tous droits réservés. L'accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

2025, arXiv (Cornell University)

We establish the relation between two objects: an integrable system related to Painlevé II equation, and the symplectic invariants of a certain plane curve Σ T W describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F GUE , governing the distribution of the maximal eigenvalue in hermitian random matrices, can also be recovered from symplectic invariants.

2025

We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F_{GUE}, governing the distribution of the maximal

2025, Ganita

The aim of this paper is to evaluate two integrals involving generalization of the H-function and employ them to obtain two Fourier Series for the generalization of the H-function. Some Fourier series for MeijerâA ˘ ´Zs G-function, MacRobert function are included as particular cases. 2010 Mathematics subject classification: 33C60, 42B05, 42C10.

2025, arXiv (Cornell University)

In this paper we define and study the moduli space of metric-graph-flows in a manifold M . This is a space of smooth maps from a finite graph to M , which, when restricted to each edge, is a gradient flow line of a smooth (and generically Morse) function on M . Using the model of Gromov-Witten theory, with this moduli space replacing the space of stable holomorphic curves in a symplectic manifold, we obtain invariants, which are (co)homology operations in M . The invariants obtained in this setting are classical cohomology operations such as cup product, Steenrod squares, and Stiefel-Whitney classes. We show that these operations satisfy invariance and gluing properties that fit together to give the structure of a topological quantum field theory. By considering equivariant operations with respect to the action of the automorphism group of the graph, the field theory has more structure. It is analogous to a homological conformal field theory. In particular we show that classical relations such as the Adem relations and Cartan formulae are consequences of these field theoretic properties. These operations are defined and studied using two different methods. First, we use algebraic topological techniques to define appropriate virtual fundamental classes of these moduli spaces. This allows us to define the operations via the corresponding intersection numbers of the moduli space. Secondly, we use geometric and analytic techniques to study the smoothness and compactness properties of these moduli spaces. This will allow us to define these operations on the level of Morse-Smale chain complexes, by appropriately counting metric-graph-flows with particular boundary conditions. 1 Categories of graphs, and the moduli space of metric-Morse structures on a graph. 7 2 The moduli space of metric-graph flows in a manifold 12

2025, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

2025, arXiv (Cornell University)

We use L 2 -Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H 1 ( S, j * V), where the local system V arises from the third primitive cohomology of family of Calabi-Yau threefolds over a curve S. The method gives a way to predict the presence of algebraic 2-cycles in the total space of the family and is applied to some examples.

2025, arXiv (Cornell University)

We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic. We prove that the images are as large as possible for almost every prime, if the Siegel cusp form is not a Maass spezialform and verifies two easy to check conditions.

2025, Nuclear Physics B

Compactification of M theory in the presence of G-fluxes yields N = 2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza-Klein reduction of the eleven-dimensional action on a Calabi-Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents fivebranes wrapped over holomorphic cycles. This solution has a "running volume" and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS 5 vacuum of the 5-dimensional supergravity.

2025, Nuclear Physics B

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the N = 2, D = 4 supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the treelevel coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi-Yau three-folds, namely the intersection numbers, the second Chern class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the nonvanishing of some of the charges and still have a finite entropy.

2025, Nuclear Physics B

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N = 2, D = 4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kähler moduli space of the IIA N = 2 vector multiplets to the quaternionic moduli space of the N = 2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kähler effective action, into IIB D-instanton solutions of the IIB quaternionic σ-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.

2025, Nuclear Physics B

We discuss general bosonic stationary configurations of N = 2, D = 4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special Kähler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the ST U model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the ST U black hole solution, in the neighbourhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N = 2 supergravity.

2025

Associated with a finite dimensional algebra of global dimension at most 2, a generalized cluster category was introduced in [Ami08]. It was shown to be triangulated, and 2-Calabi-Yau when it is Hom-finite. By definition, the cluster categories of [BMR + 06] are a special case. In this paper we show that a large class of 2-Calabi-Yau triangulated categories, including those associated with elements in Coxeter groups from [BIRS09a], are triangle equivalent to generalized cluster categories. This was already shown for some special elements in [Ami08] and then more generally for c-sortable elements in [AIRT10].