Related papers: Calabi-Yau metrics and string compactification
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
Motivated by recent progress in the problem of numerical K\"ahler metrics, we survey machine learning techniques in this area, discussing both advantages and drawbacks. We then revisit the algebraic ansatz pioneered by Donaldson. Inspired…
The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg…
We prove that Calabi-Yau metrics on compact Calabi-Yau manifolds whose Kahler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. To this end we prove an asymptotic…
We compactify $M$-theory on a Calabi-Yau manifold to five dimensions by wrapping the membrane and fivebrane solitons of the eleven-dimensional supergravity limit around Calabi-Yau two-cycles and four-cycles respectively. We identify the…
The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…
In these lecture notes, we survey the landscape of Calabi-Yau threefolds, and the use of machine learning to explore it. We begin with the compact portion of the landscape, focusing in particular on complete intersection Calabi-Yau…
We determine the N=1 low energy effective action for compactifications of type IIB string theory on compact Calabi-Yau orientifolds in the presence of background fluxes from a Kaluza-Klein reduction. The analysis is performed for Calabi-Yau…
The evidence for string/string-duality can be extended from the matching of the vector couplings to gravitational couplings. In this note this is shown in the rank three example, the closest stringy analog of the Seiberg/Witten-setup, which…
We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the…
These are lecture notes for two lectures delivered at the Les Houches workshop on Number Theory, Physics, and Geometry, March 2003. They review two examples of interesting interactions between number theory and string compactification, and…
Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy…
We construct many new examples of complete Calabi-Yau metrics of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones with smooth cross-sections. A detailed description of the geometry at infinity of these…
We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of…
We calculate one-loop string amplitudes of open and closed strings with N=1,2,4 supersymmetry in four and six dimensions, by compactification on Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine contributions from…
We study the possibility of realizing an effective sequestering between visible and hidden sectors in generic heterotic string models, generalizing previous work on orbifold constructions to smooth Calabi-Yau compactifications. In these…
Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples…
We first review standard results of the compactification of type IIA and IIB supergravities on a Calabi-Yau threefold and illustrate mirror symmetry. Then we compactify the same theories on a class of generalized Calabi-Yau manifolds called…
Certain six-dimensional (1,0) supersymmetric little string theories, when compactified on $T^3$, have moduli spaces of vacua given by smooth K3 surfaces. Using ideas of Gaiotto-Moore-Neitzke, we show that this provides a systematic…
Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics for the free case and with interaction is…