Related papers: Local B-model Yukawa couplings from A-twisted corr…
We construct heterotic standard models by compactifying on smooth Calabi-Yau three-folds in the presence of purely Abelian internal gauge fields. A systematic search over complete intersection Calabi-Yau manifolds with less than six Kahler…
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…
The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, $T_{SUSY}$, which characterizes the supersymmetric particle…
Birational Calabi-Yau threefolds in the same deformation family provide a `weak' counterexample to the global Torelli problem, as long as they are not isomorphic. In this paper, it is shown that deformations of certain desingularized…
After a brief introduction into the use of Calabi--Yau varieties in string dualities, and the role of toric geometry in that context, we review the classification of toric Calabi-Yau hypersurfaces and present some results on complete…
Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be…
We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by…
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 propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB…
Using tropical geometry we propose a mirror construction for monomial degenerations of Calabi-Yau varieties in toric Fano varieties. The construction reproduces the mirror constructions by Batyrev for Calabi-Yau hypersurfaces and by Batyrev…
Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a…
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds…
The moduli dependent Yukawa couplings between twisted sectors of the $Z_3\times Z_3$ orbifold are studied.
Given a Tyurin degeneration of a Calabi-Yau complete intersection in a toric variety, we prove gluing formulas relating the generalized functional invariants, periods, and $I$-functions of the mirror Calabi-Yau family and those of the two…
In this article, we study mirror symmetry for pairs of singular Calabi--Yau manifolds which are double covers of toric manifolds. Their period integrals can be seen as certain `fractional' analogues of those of ordinary complete…
In this paper, we derive the renormalization scale dependence of noncommutative mirror Yukawa couplings. To achieve this, we first formulate an Euclidean noncommutative version of the Yukawa sector within the electroweak-scale mirror right…
We present a new method to solve the holomorphic anomaly equations governing the free energies of type B topological strings. The method is based on direct integration with respect to the non-holomorphic dependence of the amplitudes, and…
This paper continues the authors' program of studying mirror symmetry via log geometry and toric degenerations, relating affine manifolds with singularities, log Calabi-Yau spaces, and toric degenerations of Calabi-Yaus. The main focus of…
A general method of computing string corrections to the K\"ahler metric and Yukawa couplings is developed at the one-loop level for a general compactification of the heterotic superstring theory. It also provides a direct determination of…
We use arithmetic and Hodge-theoretic techniques to study pencils of Calabi-Yau varieties realized as highly symmetric hypersurfaces in Grassmannians and their quotients, demonstrating that their geometric properties are distinct from the…