Related papers: Generalized Calabi-Yau manifolds and the chiral de…
The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…
Spectral flow, spacetime supersymmetry, topological twists, chiral primaries related to marginal deformations, mirror symmetry: these are important consequences of the worldsheet N=2 superconformal symmetry of strings on Calabi-Yau…
We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional…
We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
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 use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown that not only the metric and B-field but also the algebraic structures are uniquely…
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…
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to $\mathbb{P}^1$, namely the projective super…
The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are…
In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally…
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…
We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is…
The Kahler moduli space of a particular non-simply-connected Calabi-Yau manifold is mapped out using mirror symmetry. It is found that, for the model considered, the chiral ring may be identical for different associated conformal field…
A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…
We survey mirror symmetry of Calabi-Yau manifolds from the perspective of families of Calabi-Yau manifolds and their period integrals. Special emphasis is laid on distinguished properties of the hypergeometric series of Gel'fand, Kapranov,…
We present a universal normal algebra suitable for constructing and classifying Calabi-Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to…
We construct Calabi-Yau geometries with wrapped D6 branes which realize ${\cal N}=1$ supersymmetric $A_r$ quiver theories, and study the corresponding geometric transitions. This also yields new large $N$ dualities for topological strings…
We present a construction of the chiral de Rham complex over an algebraic surface with at most rational singularities of $A_n$-type. An explicit formula for the character of the chiral structure sheaf is also provided.
In recent work N. Hitchin introduced the concept of "generalised geometry". The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we give…