相关论文: Non-geometric Calabi-Yau compactifications and fra…

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 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)…

We generalize the cohomological mirror duality of Borcea and Voisin in any dimension and for any number of factors. Our proof applies to all examples which can be constructed through Berglund-H\"{u}bsch duality. Our method is a variant of…

We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…

We review the applications of mirror symmetry to the study of the moduli spaces of two-dimensional conformal field theories with $N{=}(2,2)$ supersymmetry, particularly those constructed from Calabi--Yau manifolds. (Lecture delivered at the…

We clarify certain important issues relevant for the geometric interpretation of a large class of N = 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly…

We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized conifold. We discuss its geometrical…

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a…

If $X$ and $Y$ are a mirror pair of Calabi--Yau threefolds, mirror symmetry should extend to an isomorphism between the type IIA string theory compactified on $X$ and the type IIB string theory compactified on $Y$, with all nonperturbative…

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two…

We study the worldsheet CFTs of type II strings on compact $G_2$ orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the…

We identify the auxiliary fields in the hypermultiplets of type IIB string theory compactified on a Calabi-Yau manifold, using a combination of worldsheet and supergravity techniques. The SUSY-breaking squark and gaugino masses in type IIB…

We construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special points in moduli spaces containing geometric limits described by non-linear sigma…

We generalize the previously established (0,2) triality of exactly solvable models, Landau-Ginzburg theories and Calabi-Yau manifolds to a number of different classes of (0,2) compactifications derived from (2,2) vacua. For the resulting…

We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The…

This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…

We show how the Landau-Ginzburg/Calabi-Yau correspondence for the quintic three-fold can be cast into a global mirror symmetry framework. Then we draw inspiration from Berglund-H\"ubsch mirror duality construction to provide an analogue…

It is known that there exist Calabi-Yau structures on the complexifications of symmetric spaces of compact type. In this paper, we describe the Calabi-Yau structures of the complexified symmetric spaces in terms of the Schwarz's theorem in…

Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not…

We discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its non-perturbative twisted chiral potential. The relevant compact part of the 4-fold…