Related papers: An Isomorphism Extension Theorem for Landau-Ginzbu…

Higher-matter is defined by higher-representation of a symmetry algebra, such as the $p$-form symmetries, higher-group symmetries or higher-categorical symmetries. In this paper, we focus on the cases of higher-group symmetries, which are…

We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =…

In this paper, we study the bigraded vector space structure of Landau-Ginzburg orbifolds. We prove the formula for the generating function of the Hodge numbers of possibly nonabelian Landau-Ginzburg orbifolds. As an application, we…

We show that there is an extra dimension to the mirror duality discovered in the early nineties by Greene-Plesser and Berglund-H\"ubsch. Their duality matches cohomology classes of two Calabi--Yau orbifolds. When both orbifolds are equipped…

In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau manifolds. These moduli spaces reflect…

Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne-Mumford stacks. More precisely, we prove that the big equivariant quantum D-module of a toric…

We study, by means of mirror symmetry, the quantum geometry of the K\"ahler-class parameters of a number of Calabi-Yau manifolds that have $b_{11}=2$. Our main interest lies in the structure of the moduli space and in the loci corresponding…

We study Lie bialgebra structures on \emph{flat metric Lie algebras}, that is, Lie algebras $(\mathfrak{g},\langle\cdot,\cdot\rangle)$ whose associated left-invariant Riemannian metric on the simply connected Lie group $G$ has zero…

Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau--Ginzburg orbifolds. Namely, for the pairs $(f,G)$, where $f$…

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…

We are considering the class of heterotic $\mathcal{N}=(2,2)$ Landau-Ginzburg orbifolds with 9 fields corresponding to $A_1^9$ Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under…

In this paper we discuss correlation function computations in massive topological Landau-Ginzburg orbifolds, extending old results of Vafa. We then apply these computations to provide further tests of the nonabelian mirrors proposal and…

We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural functor from the Fukaya category to the category of matrix…

We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed…

Let $V$ and $W$ be finite dimensional real vector spaces and let $G\subset\GL(V)$ and $H\subset\GL(W)$ be finite subgroups. Assume for simplicity that the actions contain no reflections. Let $Y$ and $Z$ denote the real algebraic varieties…

We investigate strings at singularities of G_2-holonomy manifolds which arise in Z_2 orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R^4/Z_2 fibered over a SLAG, and can globally be embedded in CICYs in…

In this paper we extend the nonabelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of O(k) gauge groups with discrete theta angles. We check our proposed extension by…

We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold $X$ degenerates to a union of two quasi-Fano manifolds (Tyurin…

We calculate the B-model on the mirror pair of $X_{2N-2}(2,2,\cdots,2,1,1)$ , which is an $(N-2)$-dimensional Calabi-Yau manifold and has two marginal operators i.e. $h^{1,1}(X_{2N-2}(2,2,\cdots,2,1,1))=2$. In \cite{nagandjin} we have…

An invertible polynomial in $n$ variables is a quasihomogeneous polynomial consisting of $n$ monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric…