Kazushi Ueda, Yutaka Yoshida
We compute genus-zero Gromov--Witten invariants of Calabi--Yau complete intersection 3-folds in Grassmannians using supersymmetric localization in A-twisted non-Abelian gauged linear sigma models. We also discuss a Seiberg-like duality interchanging Gr(n,m) and Gr(m-n,m).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in the math community. For symplectic Grassmannians, we check that the Coulomb branch vacua of the GLSM are consistent with ordinary and equivariant quantum cohomology of the space.
Schubert defects in Lagrangian Grassmannians
本文借鉴已有研究提出拉格朗日格拉斯曼流形中对应舒伯特闭链的GLSM缺陷构造方法，通过多维度对比验证了该构造的合理性，为相关数学物理研究提供新的构造思路。
In this paper we give gauged linear sigma model (GLSM) realizations of a number of geometries not previously presented in GLSMs. We begin by describing GLSM realizations of maps including Veronese and Segre embeddings, which can be applied to give GLSMs explicitly describing constructions such as the intersection of one hypersurface with the image under some map of another. We also discuss GLSMs for intersections of Grassmannians and Pfaffians with one another, and with their images under various maps, which sometimes form exotic constructions of Calabi-Yaus, as well as GLSMs for other exotic …
In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances…
In this paper, we apply recent methods of localized GLSMs to make predictions for Gromov-Witten invariants of noncommutative resolutions, as defined by e.g. Kontsevich, and use those predictions to examine the connectivity of the SCFT moduli space. Noncommutative spaces, in the present sense, are defined by their sheaves, their B-branes. Examples of abstract CFT's whose B-branes correspond with those defining noncommutative spaces arose in examples of abelian GLSMs describing branched double covers, in which the double cover structure arises nonperturbatively. This note will examine the GLSM f…
Revisiting three-dimensional GLSMs and K-theoretic I-functions
本文重新审视三维规范线性sigma模型与K理论Gromov-Witten理论的对应关系，证明格拉斯曼流形的K理论Hori-Vafa公式源于含反常消除因子的三维规范理论，并推导了各向同性格拉斯曼流形的K理论I函数。
Grothendieck lines in 3d $\mathcal{N}=2$ SQCD and the quantum K-theory of the Grassmannian
本文从线缺陷视角重新研究三维N=2 SQCD中格拉斯曼流形的等变量子K理论，识别出流向舒伯特簇结构层的格罗滕迪克线缺陷，并通过1d Witten指标给出舒伯特类基的物理实现，进而显式计算量子K理论环及相关计数不变量。
GLSM monodromy on quantum period lattice of Calabi-Yau fourfold flops
本文利用 GLSM 的等级限制规则和窗口范畴，建立了 Calabi-Yau 四维翻转的 B 膜中心电荷整基，推导其单值性精确表达式，将单值性解释为 EZ 扭转，并说明该扭转可分解为相关构型族的球形扭转。
We study two-dimensional $\mathcal{N}{=}(0,2)$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider $\mathcal{N}{=}(0,2)$ theories with an $R$-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of $\mathcal{N}{=}(2,2)$ GLSMs and retain a Coulomb branch, we consider the $A/2$-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators awa…
We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov-Witten invariants ($g \leq 5$) of the derived equivalent Calabi-Yau threefolds, which are of the appropriate codimensions in the Grassmannian Gr(2,7) and the Pfaffian Pf(7).
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental factorization" supported on the moduli space of Landau-Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the associated map on Hochschild homology defines our theory.
We propose Picard-Fuchs equations for periods of nonabelian mirrors in this paper. The number of parameters in our Picard-Fuchs equations is the rank of the gauge group of the nonabelian GLSM, which is eventually reduced to the actual number of Kähler parameters. These Picard-Fuchs equations are concise and novel. We justify our proposal by reproducing existing mathematical results, namely Picard-Fuchs equations of Grassmannians and Calabi-Yau manifolds as complete intersections in Grassmannians. Furthermore, our approach can be applied to other nonabelian GLSMs, so we compute Picard-Fuchs equ…
On genus-0 invariants of Calabi-Yau hybrid models
本文计算了卡拉比-丘规范线性sigma模型混合相的亏格0关联函数，通过提取I函数和J函数并利用场论识别插入状态，验证了结果与镜像对称及FJRW理论一致。
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 …
We give two proofs of a conjecture of Hori and Vafa which expresses the J-function (i.e, the generating function for 1-point descendant Gromov-Witten invariants) of a Grassmannian in terms of the J-function of a product of projective spaces. Similar relations are obtained for two-point descendants, and three-point (primary) Gromov-Witten invariants. As an application we prove Givental's "R-Conjecture" - hence the Virasoro conjecture - for Grassmannians.
We construct a mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete intersection X and the Landau-Ginzburg dual (FJRW-theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau-Ginzburg/Calabi-Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic th…
In this paper we investigate the tau-functions for the stationary sector of Gromov-Witten theory of the complex projective line and its version, relative to one point. In particular, we construct the integral representation for the points of the Sato Grassmannians, Kac-Schwarz operators, and quantum spectral curves. This allows us to derive the matrix models.
There is a set of remarkable physical predictions for the structure of BCOV's higher genus B-model of mirror quintic 3-folds which can be viewed as conjectures for the Gromov-Witten theory of quintic 3-folds. They are (i) Yamaguchi--Yau's finite generation, (ii) the holomorphic anomaly equation, (iii) the orbifold regularity and (iv) the conifold gap condition. Moreover, these properties are expected to be universal properties for all the Calabi-Yau 3-folds. This article is devoted to proving first three conjectures. The main geometric input to our proof is a log GLSM moduli space and the comp…
Elliptic and genus one fibered Calabi-Yau spaces play a prominent role in string theory and mathematics. In this article we discuss a class of genus one fibered Calabi-Yau threefolds with 5-sections from various perspectives. In algebraic geometry, such Calabi-Yaus can be constructed as complete intersections in Grassmannian fibrations and as Pfaffian varieties. These constructions naturally fit into the framework of homological projective duality and lead to dual pairs of Calabi-Yaus. From a physics perspective, these spaces can be realised as low-energy configurations ("phases") of gauged li…
We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of $gl(K_1,K_2|M)$ superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generaliz…
In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the ${\cal I}$ and ${\cal J}$-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show h…
Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
该研究证明了格拉斯曼流形$\text{Gr}(k;n)$环面等变量子K理论的惠特尼与库仑分支两种表示，建立二者代数关联，并计算了其tautological丛外幂的K理论格罗莫夫-威滕不变量。
In this work we study the quantum periods together with their Picard-Fuchs differential equations of Calabi-Yau fourfolds. In contrast to Calabi-Yau threefolds, we argue that the large volume points of Calabi-Yau fourfolds generically are regular singular points of the Picard-Fuchs operators of non-maximally unipotent monodromy. We demonstrate this property in explicit examples of Calabi-Yau fourfolds with a single Kahler modulus. For these examples we construct integral quantum periods and study their global properties in the quantum Kahler moduli space with the help of numerical analytic con…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。