Topological String on Toric CY3s in Large Complex Structure Limit

We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that purpose, we first consider the $T^{2}\times R$ special Lagrangian fibration of generic CY3-folds and we give the realization of the class of large $\mu$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials $)$. Then, we focus on a one complex parameter supersymmetric $U(1)$ gauged model involving six chiral superfields ${\Phi_{i}}$ with $\mathcal{W}=\mu (\prod\nolimits_{i=0}^{5}\Phi_{i})$ and we use it to compute the function $\mathcal{Z}_{top}$ for the case of the local elliptic curve in the limit $\mu \to \infty$.Comment: Latex, 38 pages, 12 figures. To appear in Nucl Phys

Mirror Symmetry for Hypersurfaces in Weighted Projective Space and Topological Couplings

By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the corresponding coupling on the mirror model in the large complex structure limit.Comment: 28p, use harvmac. A new derivation of the Yukawa coupling in the large complex structure limit has been added to section 5.

On Mirror Symmetry for Calabi-Yau Fourfolds with Three-Form Cohomology

We study the action of mirror symmetry on two-dimensional N=(2,2) effective theories obtained by compactifying Type IIA string theory on Calabi-Yau fourfolds. Our focus is on fourfold geometries with non-trivial three-form cohomology. The couplings of the massless zero-modes arising by expanding in these forms depend both on the complex structure deformations and the Kahler structure deformations of the Calabi-Yau fourfold. We argue that two holomorphic functions of the deformation moduli capture this information. These are exchanged under mirror symmetry, which allows us to derive them at the large complex structure and large volume point. We discuss the application of the resulting explicit expression to F-theory compactifications and their weak string coupling limit. In the latter orientifold settings we demonstrate compatibility with mirror symmetry of Calabi-Yau threefolds at large complex structure. As a byproduct we find an interesting relation of no-scale like conditions on Kahler potentials to the existence of chiral and twisted-chiral descriptions in two dimensions.Comment: 36 page

On the Flux Vacua in F-theory Compactifications

We study moduli stabilization of the F-theory compactified on an elliptically fibered Calabi-Yau fourfold. Our setup is based on the mirror symmetry framework including brane deformations. The complex structure moduli dependence of the resulting 4D N=1 effective theory is determined by the associated fourfold period integrals. By turning on appropriate G-fluxes, we explicitly demonstrate that all the complex structure moduli fields can be stabilized around the large complex structure point of the F-theory fourfold.Comment: 5 pages, v2: published versio

Group actions, non-K\"ahler complex manifolds and SKT structures

We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-K\"ahler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-K\"ahler) complex structures on tangential frame bundles of complex orbifolds.Comment: A new Section 4 is adde

Combination of large nanostructures and complex band structure for high performance thermoelectric lead telluride

The complexity of the valence band structure in p-type PbTe has been shown to enable a significant enhancement of the average thermoelectric figure of merit (zT) when heavily doped with Na. It has also been shown that when PbTe is nanostructured with large nanometer sized Ag_2Te precipitates there is an enhancement of zT due to phonon scattering at the interfaces. The enhancement in zT resulting from these two mechanisms is of similar magnitude but, in principle, decoupled from one another. This work experimentally demonstrates a successful combination of the complexity in the valence band structure with the addition of nanostructuring to create a high performance thermoelectric material. These effects lead to a high zT over a wide temperature range with peak zT > 1.5 at T > 650 K in Na-doped PbTe/Ag_2Te. This high average zT produces 30% higher efficiency (300–750 K) than pure Na-doped PbTe because of the nanostructures, while the complex valence band structure leads to twice the efficiency as the related n-type La-doped PbTe/Ag_2Te without such band structure complexity