Related papers: Toric Geometry and Calabi-Yau Compactifications
We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz…
We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the…
We demonstrate that type II string theory compactified on a singular Calabi-Yau manifold is related to $c=1$ string theory compactified at the self-dual radius. We establish this result in two ways. First we show that complex structure…
We identify a class of autoequivalences of triangulated categories of singularities associated with Calabi-Yau complete intersections in toric varieties. Elements of this class satisfy relations that are directly linked to the toric data.
Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi-Yau hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed polytopes with a minimal number of facets and of inscribed…
The parameter-space orbifold construction of open and unoriented toroidal and (target-space) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral four-dimensional type-I…
Geometric transitions between Calabi-Yau manifolds have proven to be a powerful tool in exploring the intricate and interconnected vacuum structure of string compactifications. However, their role in N=1, 4-dimensional string…
In this paper we start the program of constructing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric variety near the large complex limit, with respect to the restriction of a toric metric on the toric…
We consider the construction of Calabi-Yau varieties recently generalized to where the defining equations may have negative degrees over some projective space factors in the embedding space. Within such "generalized complete intersection"…
Two-dimensional hybrid superstring on singular Calabi-Yau manifolds is studied by the field redefinition of the NSR formalism. The compactification on singular Calabi-Yau fourfold is described by N=2 super-Liouville theory and N=2…
We develop some methods to construct normal crossing varieties whose dual complexes are two-dimensional, which are smoothable to Calabi--Yau threefolds. We calculate topological invariants of smoothed Calabi--Yau threefolds and show that…
We review various constructions of mirror symmetry in terms of Landau-Ginzburg orbifolds for arbitrary central charge $c$ and \CY\ hypersurfaces and complete intersections in toric varieties. In particular it is shown how the different…
We review advancements in deep learning techniques for complete intersection Calabi-Yau (CICY) 3- and 4-folds, with the aim of understanding better how to handle algebraic topological data with machine learning. We first discuss…
A fundamental step towards studying string theory vacua, and, ultimately, their stability, is that of understanding the underlying mathematical structure of the QFT resulting from its dimensional reduction on Calabi-Yau (CY) manifolds, the…
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly…
After a quick review of the wild structure of the complex moduli space of Calabi-Yau threefolds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of "deformation equivalence" for geometric transitions is…
A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This approach is informed by homological mirror symmetry, derived…
We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the…
We review cosmological solutions of type II superstrings and M-theory, emphasizing the role of non-vanishing Ramond form backgrounds. Compactifications on flat and, more generally, maximally symmetric spatial subspaces are presented. We…
We generalize the standard combinatorial techniques of toric geometry to the study of log Calabi-Yau surfaces. The character and cocharacter lattices are replaced by certain integral linear manifolds described by Gross, Hacking, and Keel,…