Related papers: Complete Calabi-Yau metrics from Kahler metrics in…

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and…

We explicitly construct and study the statistics of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau hypersurface $P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. We solve for these moduli…

Calabi-Yau spaces, or Kahler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half-century. In physics, they constituted the first and natural solution to…

We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over…

The Kahler potential is the least understood part of effective N=1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kahler potential for the physical matter fields, as a function of the moduli fields,…

Let $X$ be a compact K\"ahler manifold and $S$ a subvariety of $X$ with higher co-dimension. The aim is to study complete constant scalar curvature K\"ahler metrics on non-compact K\"ahler manifold $X-S$ with Poincar\'e--Mok--Yau asymptotic…

Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…

Given a K\"ahler manifold $M$ endowed with a Hamiltonian Killing vector field $Z$, we construct a conical K\"ahler manifold $\hat{M}$ such that $M$ is recovered as a K\"ahler quotient of $\hat{M}$. Similarly, given a hyper-K\"ahler manifold…

In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where…

In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a solution of the Strominger system and the equations of motion of heterotic string…

On an affine flat manifold with coordinates x^j and convex local potential function f, we call the affine Kahler metric f_{ij} dx^i dx^j semi-flat Calabi-Yau if it satisfies det f_{ij} = 1. Recently Gross-Wilson have constructed many such…

Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of…

In this paper we discuss four methods of proving modularity of Calabi--Yau threefolds with $h^{12}=1$: existence of elliptic ruled surfaces inside (Hulek-Verrill), correspondence with a product of an elliptic curve and a K3 surface…

We find new examples of compact Spin(7)-manifolds using a construction of Joyce. The essential ingredient in Joyce's construction is a Calabi-Yau 4-orbifold with particular singularities admitting an antiholomorphic involution, which fixes…

Quantum non-perturbative geometry of the universal hypermultiplet is investigated. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the universal…

A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in…

We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is…

We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$. Solutions include nearly-K\"ahler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds.…

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 probe the existence of supersymmetric vacua of the type IIB orientifold of the elliptic Calabi-Yau space P_{11169}[18] where generically two complex structure moduli z_i, the dilaton tau and the two K\"ahler moduli T_i are stabilized by…