Eran Palti
We study intersecting D6-branes in Calabi-Yau manifolds that are smooth hypersurfaces in weighted projective spaces. We develop the techniques for calculating intersection numbers between special Lagrangian sub-manifolds defined as fixed loci of anti-holomorphic involutions. We present global Pati-Salam and MSSM-like models that are supersymmetric up to a decoupled hidden sector.
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In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as "1/2 Calabi-Yau 3-folds". We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields a novel approach to build elliptically fibered Calabi-Yau 3-folds of various Mordell-Weil ranks. Our construction of Calabi-Yau 3-folds can be considered as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to seven $U(1)$s form in six-dimensional $N=1$ F-theory on the constructed C…
We discuss some aspects of F-theory in four dimensions on elliptically fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A particularly simple class of such manifolds emerges for fourfolds in which the generic Calabi-Yau threefold fiber is itself an elliptic fibration and is K3 fibered. Duality between F-theory compactified on Calabi-Yau fourfolds and heterotic strings on Calabi-Yau threefolds puts constraints on the cohomology of the fourfold. By computing the Hodge diamond of Calabi-Yau fourfolds we provide first numerical evidence for F-theory dualities in four dimensi…
Updates on Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds
本文介绍通过平滑拟Fano流形法向交叉并集构造Calabi-Yau流形的进展，给出具无界第二贝蒂数、极小赫奇数的Calabi-Yau三维流形及高维非凯勒示例，阐释Landau-Ginzburg模型在镜像构造中的作用
It is shown that the model X_{14}(7,3,2,1,1) has two Calabi--Yau phases.
In this study, four-dimensional $N=1$ F-theory models with multiple U(1) gauge group factors are constructed. A class of rational elliptic 4-folds, which we call as "$\frac{1}{2}$Calabi-Yau 4-folds," is introduced, and we construct the elliptically fibered 4-folds by utilizing them. This yields a novel approach for building families of elliptically fibered Calabi-Yau 4-folds with positive Mordell-Weil ranks. The introduced $\frac{1}{2}$Calabi-Yau 4-folds possess the characteristic property wherein the sum of the ranks of the singularity type and the Mordell-Weil group is always equal to six. T…
We study quantum Kahler moduli space of Calabi-Yau fourfolds. Our analysis is based on the recent work by Jockers et al. which gives a novel method to compute the Kahler potential on the quantum Kahler moduli space of Calabi-Yau manifold. In contrast to Calabi-Yau threefold, the quantum nature of higher dimensional Calabi-Yau manifold is yet to be fully elucidated. In this paper we focus on the Calabi-Yau fourfold. In particular, we conjecture the explicit form of the quantum-corrected Kahler potential. We also compute the genus zero Gromov-Witten invariants and test our conjecture by comparin…
We consider generic features of eleven dimensional supergravity compactified down to five dimensions on an arbitrary Calabi-Yau threefold.
We continue to develop our method for effectively computating the special Kähler geometry on the moduli space of Calabi-Yau manifolds. We generalize it to all polynomial deformations of Fermat hypersurfaces.
It has recently been realized that a large class of Calabi-Yau models in which the VEV of the gauge connection is not set equal to the spin connection of the Calabi-Yau manifold are valid classical solutions of string theory. We provide some examples of three generation models based on such generalized Calabi-Yau compactifications, including models with observable gauge group $SU(3)\times SU(2)\times U(1)$.
We study when Calabi-Yau supermanifolds M(1|2) with one complex bosonic coordinate and two complex fermionic coordinates are super Ricci-flat, and find that if the bosonic manifold is compact, it must have constant scalar curvature.
Long ago, Nemeschansky and Sen demonstrated that the Ricci-flat metric on a Calabi-Yau manifold could be corrected, order by order in perturbation theory, to produce a conformally invariant (2,2) nonlinear sigma model. Here we extend this result to (0,2) sigma models for stable holomorphic vector bundles over Calabi-Yaus.
Compactifications of F-Theory on Calabi-Yau Fourfolds
通过toric几何研究F理论在卡比别四维流形上的紧化中增强的规范群。
Open topological string partition function on compact Calabi-Yau threefolds satisfies the extended holomorphic anomaly equation. By direct integration, we solve these equations and obtain partition functions for first several genus and boundaries on complete intersection Calabi-Yau threefolds. Complemented by the unoriented worldsheet contribution, the annulus functions encode the genus one BPS invariants.
We construct Calabi-Yau manifolds and their mirrors from K3 surfaces. This method was first developed by Borcea and Voisin. We examined their properties torically and checked mirror symmetry for Calabi-Yau 4-fold case. From Borcea-Voisin 3-fold or 4-fold examples, it may be possible to probe the S-duality of Seiberg -Witten.
We construct a wide class of non-geometric compactifications of type II superstring theories preserving N=1 space-time supersymmetry in four dimensions, starting from Calabi-Yau compactifications at Gepner points. Particular examples of this construction provide quantum equivalences between Calabi-Yau compactifications and non-Calabi-Yau ones, generalizing mirror symmetry. The associated Landau-Ginzburg models involve both chiral and twisted chiral multiplets hence cannot be lifted to ordinary Calabi-Yau gauged linear sigma-models.
In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi-Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi-Yau geometry, the recipe automatically generalizes for divisors in other Calabi-Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi-Yau geometry in the large volume regime. Finally we extract the…
We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.
Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.
We use Serre construction and deformation to construct stable bundles and reflexive sheaves on Calabi-Yau threefolds.
There are easy "polynomial" deformations of Calabi-Yau hypersurfaces in toric varieties performed by changing the coefficients of the defining polynomial of the hypersurface. In this paper, we explicitly constructed the ``non-polynomial'' deformations of Calabi-Yau hypersurfaces, which arise from deformations of the ambient toric variety.
We study the limit of Calabi-Yau modular forms, and in particular, those resulting in classical modular forms. We then study two parameter families of elliptically fibred Calabi-Yau fourfolds and describe the modular forms arising from the degeneracy loci. In the case of elliptically fibred Calabi-Yau threefolds our approach gives a mathematical proof of many observations about modularity properties of topological string amplitudes starting with the work of Candelas, Font, Katz and Morrison. In the case of Calabi-Yau fourfolds we derive new identities not computed before.
We show that "non-polynomial" deformations of semiample (minimal) nondegenerate Calabi-Yau hypersurfaces in complete simplicial toric varieties can be realized as quasismooth complete intersections in higher dimensional simplicial toric varieties.
We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric Calabi-Yau 3-folds, and show that they are ordinary weak Jacobi forms given by an explicit formula predicted by Eguchi and Sugawara.
The elliptic quasimap potential function is explicitly calculated for Calabi-Yau complete intersections in projective spaces by Kim and Lho. We extend this result to local Calabi-Yau varieties. Using this as well as the wall crossing formula by Ciocan-Fontanine and Kim, we can calculate the elliptic Gromov-Witten potential function.
In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.
Any Calabi-Yau threefold X with infinite fundamental group admits an étale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the latter case. In this paper, we provide the full classification of Calabi-Yau threefolds of type K, based on Oguiso and Sakurai's work. Together with a refinement of Oguiso and Sakurai's result on Calabi-Yau threefolds of type A, we finally complete the classification of Calabi-Yau threefolds with infinite fundamental group.
Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
本研究在第五后闵可夫斯基阶的四环费曼积分中发现卡拉比-丘三维流形，揭示该阶黑洞散射解析结果会出现全新函数，为双黑洞并合引力波相关研究提供新的几何视角。
We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kahler base. For any 2d-dimensional Calabi-Yau cone, we find explicit solutions of the flow equations that correspond to non-trivial SU(d) HYM instantons. These can be regarded as deformations of the spin connection of the Calabi-Yau cone.
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in CP5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holom…
We study a direct flux breaking scenario in $SO(32)$ heterotic string theory on general Calabi-Yau threefolds. The direct flux breaking, corresponding to hypercharge flux breaking in the F-theory context, allows us to derive the Standard Model in general Calabi-Yau compactifications. We present a general formula leading to the three generations of quarks and leptons and no chiral exotics in a background-independent way. As a concrete example, we show the three-generation model on a complete intersection Calabi-Yau threefold.
We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds.
We study Calabi-Yau compactifications of non relativistic string theory and show that it can be derived from the corresponding relativistic Calabi-Yau compactifications by taking the non relativistic limit of the resulting 4D theory without changing the internal part.
The open string sector of the topological B-model on CY $(m+2)$-folds is described by $m$-graded quivers with superpotentials. This correspondence generalizes the connection between CY $(m+2)$-folds and gauge theories on the worldvolume of D$(5-2m)$-branes for $m=0,\ldots,3$ to arbitrary $m$. In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CY$_{m+2}$ and CY$_{n+2}$ produces the quiver theory for a related CY$_{m+n+3}$. This method significantly supersedes existing ones, enabling the simple determination of quiv…
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank 2 and 4 constructed out of pure geometric data of the given Calabi-Yau space. As an application, we find that some of these bundles satisfy the physical constraint imposed by heterotic string anomaly cancellation.
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers
针对卡拉比-丘三维流形构造需求，提出基于Transformer的CYTransformer模型，可自动高效无偏生成FRST并自我改进，为社区平台AICY探索卡拉比-丘图景奠定基础。
We identify a class of autoequivalences of triangulated categories of singularities associated with Calabi-Yau complete intersections in toric varieties. Elements of this class satisfy relations that are directly linked to the toric data.
We show that Calabi-Yau manifolds are emergent from the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons. Therefore we argue that the noncommutative Hermitian U(1) instantons correspond to quantized Calabi-Yau manifolds.
We consider Laplace transforms of the Picard-Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms of Gel'fand-Kapranov-Zelevinski hypergeometric systems.
Calabi-Yau Deformation Quantization
研究卡拉比-丘流形的变形量子化，通过记录孔采维奇形式性态射的卡拉比-丘流形版本，发现单模全纯泊松卡拉比-丘流形有典范闭变形量子化，旨在借助森-兹维巴赫弦顶点在该范畴解释孔采维奇变形量子化。
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