Related papers: Singular Calabi-Yau Manifolds and ADE Classificati…
Two-dimensional hybrid superstring on singular Calabi-Yau manifolds is studied by the field redefinition of the NSR formalism. The compactification on singular Calabi-Yau fourfold is described by N=2 super-Liouville theory and N=2…
We consider the compactification of the IIA string to (1+1) dimensions on non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the compactification include 4-form fluxes, and a particular class of these models has been…
We investigate a Gepner-like superstring model described by a combination of multiple minimal models and an N=2 Liouville theory. This model is thought to be equivalent to the superstring theory on a singular noncompact Calabi-Yau manifold.…
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…
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma models on toric Calabi-Yau manifolds. We derive and solve new constraint equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on the…
We consider type II and heterotic string compactifications on an isolated singularity in the noncompact Gepner model approach. The conifold-type ADE noncompact Calabi-Yau threefolds, as well as the ALE twofolds, are modeled by a tensor…
When we describe non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the modular transformations. In this article, we…
In this paper we discuss various aspects of non-compact models of CFT of the type: $ \prod_{j=1}^{N_L} {N=2 Liouville theory}_j \otimes \prod_{i=1}^{N_M} {N=2 minimal model}_i $ and $ \prod_{j=1}^{N_L}{SL(2;R)/U(1) supercoset}_j \otimes…
We study the type II superstring theory on the background $\br^{d-1,1}\times X_n$, where $X_n$ is a Calabi-Yau $n$-fold ($2n+d=10$) with an isolated singularity, by making use of the holographically dual description proposed by…
We study some properties of a singular Landau-Ginzburg family characterized by the multi-variable superpotential $W=-X^{-1}(Y_1Y_2)^{n-1} + {1\over n} (Y_1Y_2)^n - Y_3Y_4$. We will argue that (the infra-red limit of) this theory describes…
The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg…
Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f-twisted Sobolev spaces for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration…
We investigate a class of (2,2) supersymmetric string vacua which may be represented as Landau--Ginzburg theories with a quasihomogeneous potential which has an isolated singularity at the origin. There are at least three thousand distinct…
We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain much of Intriligator and Wecht's ADE classification of $\N=1$ superconformal theories which arise as RG fixed points of $\N = 1$ SQCD theories with…
We utilize the deformation theory of algebraic singularities to study charged matter in compactifications of M-theory, F-theory, and type IIa string theory on elliptically fibered Calabi-Yau manifolds. In F-theory, this description is more…
We observe that the state space of Landau-Ginzburg isolated singularities is simply a special case of Chen-Ruan orbifold cohomology relative to the generic fibre of the potential. This leads to the definition of the cohomology of hybrid…
We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth)…
When we describe string propagation on non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the modular…
We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it for del Pezzo surfaces and coverings of projective spaces of index one. For the coverings of degree…
The recent classification of Landau--Ginzburg potentials and their abelian symmetries focuses attention on a number of models with large positive Euler number for which no mirror partner is known. All of these models are related to…