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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…
In a previous publication, arXiv:1106.4804, we have found 200 models from heterotic Calabi-Yau compactifications with line bundles, which lead to standard models after taking appropriate quotients by a discrete symmetry and introducing…
Superstring theories are the most promising theories for unified description of all fundamental interactions including gravity. However, these theories are formulated consistently only in 10 spacetime dimensions. Therefore, to connect to…
We explicitly construct the largest dataset to date of heterotic vacua arising from stable vector bundles on Calabi-Yau threefolds. Focusing on elliptically fibered Calabi-Yau manifolds with spectral cover bundles, we show that the number…
In a previous paper, we introduced a heterotic standard model and discussed its basic properties. This vacuum has the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate fields and a small number of uncharged moduli. In…
We study topological gauge theories with N=(2,0) supersymmetry based on stable bundles on general Kahler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual…
We study compactifications of F-theory on certain Calabi--Yau threefolds. We find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get promoted to $N=1$ dualities between heterotic string and F-theory in 6 dimensions. The…
We study two aspects of the physics of heterotic Line Bundle Standard Models on smooth Calabi-Yau threefolds. First, we investigate to what degree modern moduli stabilization scenarios can affect the standard model spectrum in such…
We study the possibility of obtaining metastable de Sitter vacua of heterotic string theory compactified on a Calabi-Yau threefold which are classical and simple in the K\"ahler moduli sector of the theory. For this, we exploit a known…
We modify a recently proposed heterotic model hep-th/0703210, giving three net-generations of standard model fermions, to get rid of an additional U(1) factor in the gauge group. The method employs a stable SU(5) bundle on a Calabi-Yau…
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 noncompact Calabi-Yau threefolds, their moduli spaces of vector bundles and deformation theory. We present Calabi-Yau threefolds that have infinitely many distinct deformations, constructing them explicitily, and describe the…
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the…
We argue that compactifications on Calabi-Yau threefolds with vanishing Euler number yield effective four dimensional theories exhibiting (spontaneously broken) N=4 supersymmetry. To this end, we derive the low-energy effective action for…
We derive an approximate analytic relation between the number of consistent heterotic Calabi-Yau compactifications of string theory with the exact charged matter content of the standard model of particle physics and the topological data of…
We briefly review attempts to construct string theories that yield the standard model, concentrating on models with a geometric interpretation. Calabi-Yau compactifications are discussed in the context of both the weakly coupled heterotic…
A class of abelian fibered Calabi-Yau threefolds X_{m,n} is shown yield SU(2) structure, in addition to the standard SU(3) holonomy. Compactification of type II string theory on a manifold in this class give a 4D effective supergravity…
We discuss a simple example of an F-theory compactification on a Calabi-Yau fourfold where background fluxes, together with nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes, allow us to fix all closed and…
We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second…
Motivated by the Strominger-Yau-Zaslow conjecture, we study fibre spaces whose total space has trivial canonical bundle. Especially, we are interest in Calabi-Yau varieties with fibre structure. In this paper, we only consider semi-stable…