Related papers: Modular Constraints on Calabi-Yau Compactification…

We relate the counting of refined BPS numbers on compact elliptically fibred Calabi-Yau threefolds $X$ to Wilson loop expectations values in the gauge theories that emerge in various rigid local limits of the 5d supergravity theory defined…

In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is…

We argue that in type IIB LVS string models, after including the leading order moduli stabilisation effects, the moduli space for the remaining flat directions is compact due the Calabi-Yau K\"ahler cone conditions. In cosmological…

Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau…

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\"ahler manifolds correspond to certain (abstract)…

We show that a large class of supersymmetric compactifications, including all simply connected Calabi-Yau and G_2 manifolds, have classical configurations with negative energy density as seen from four dimensions. In fact, the energy…

We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi--Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact…

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in $N=2$ supergravity theories. We discuss the symmetry…

We investigate special compactifications of the heterotic string for which the space of half-BPS states is, in a natural way, a representation of various subgroups of the Conway group. These compactifications provide a useful framework for…

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.…

Starting from the K\"ahler moduli space of the rigid orbifold Z=E^3/\mathbb{Z}_3 one would expect for the cohomology of the generalized mirror to be a Hodge structure of Calabi-Yau type (1,9,9,1). We show that such a structure arises in a…

We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds. In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with…

We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the K\"ahler moduli. This class of models corresponds to…

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…

We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open…

We develop a combinatorial approach to the construction of general smooth compact base surfaces that support elliptic Calabi-Yau threefolds. This extends previous analyses that have relied on toric or semi-toric structure. The resulting…

We present a general method for calculating the moduli spaces of fivebranes wrapped on holomorphic curves in elliptically fibered Calabi-Yau threefolds, in particular, in the context of heterotic M theory. The cases of fivebranes wrapped…

We study attractor points for Calabi-Yau variations of Hodge structures. In particular, for certain moduli spaces which are Shimura varieties, we prove that the attractor points are CM points, thus proving Moore's Attractor Conjecture in…

We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT's corresponding to T^2 target and identify the Cardy…

We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kahler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the…