Related papers: A single point as a Calabi-Yau zerofold
The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a higher dimensional generalization of non-symplectic involutions on $K3$ surfaces. We present some elementary facts about Calabi-Yau threefolds with non-Gorenstein…
We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility…
Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been…
Generalizing the work of Sen, we analyze special points in the moduli space of the compactification of the F-theory on elliptically fibered Calabi-Yau threefolds where the coupling remains constant. These contain points where they can be…
The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in…
We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching…
We consider F-theory and M-theory compactifications on singular Calabi-Yau fourfolds with an SU(5) singularity. On the M-theory side this realizes three-dimensional N=2 supersymmetric gauge theories with matter, and compactification on a…
We describe a Lie Algebra on the moduli space of Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological…
A large class of (0,2) Calabi-Yau $\sigma$-models and Landau-Ginzburg orbifolds are shown to arise as different ``phases'' of supersymmetric gauge theories. We find a phenomenon in the Landau-Ginzburg phase which may enable one to…
We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of inner automorphisms of Courant algebroids. The zero locus of our moment map is given by the solutions of the…
Calabi-Yau manifolds have played a key role in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very little is known about the explicit metrics…
We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over $\F_3$ that does not…
Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk…
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We…
It has been conjectured that the hemisphere partition function arXiv:1308.2217, arXiv:1308.2438 in a gauged linear sigma model (GLSM) computes the central charge arXiv:math/0212237 of an object in the bounded derived category of coherent…
We investigate the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11 which arise as fibre products of rational elliptic surfaces. For this purpose, we apply a method by Serre to compare two-dimensional 2-adic…
The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are…
The main aim of the paper is to develop the "Floer theory" associated to Calabi-Yau 3-folds, exending the analogy of Thomas' "holomorphic Casson invariant". The treatment in the body of the paper is largely formal, assuming appropriate…
We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ with fluxes, where $X$ is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of…
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…