Related papers: Fano hypersurfaces and Calabi-Yau supermanifolds
The SO(10) embedding of the Standard Model spectrum is supported by evidence for neutrino masses. This thesis adapts the available formalism to study a class of heterotic M-theory vacua with SO(10) grand unification group. Compactification…
The classifications of locally strongly convex equiaffine hypersurfaces (resp. centroaffine hypersurfaces) with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Blaschke-Berwald affine metric (resp. centroaffine…
For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open…
We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a…
By blowing up the ambient space along the curve wrapped by B-branes, we study the brane superpotentials and Ooguri-Vafa invariants on complete intersections Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials are…
In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov-Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections. This…
Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories…
We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces…
We consider splitting type phase transitions between Calabi-Yau fourfolds. These transitions generalize previously known types of conifold transitions between threefolds. Similar to conifold configurations the singular varieties mediating…
We consider Landau-Ginzburg (LG) models with boundary conditions preserving A-type N=2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the…
We study compact non-supersymmetric Z_N orbifolds in various dimensions. We compute the spectrum of several tachyonic type II and heterotic examples and partially classify tachyon-free heterotic models. We also discuss the relation to…
We examine the physical significance of torsion co-cycles in the cohomology of a projective Calabi-Yau three-fold for the (2,2) superconformal field theory (SCFT) associated to the non-linear sigma model with such a manifold as a target…
In this paper we analyze and classify the totally geodesic subspaces of finite volume quaternionic hyperbolic orbifolds and their generalizations, locally symmetric orbifolds arising from irreducible lattices in Lie groups of the form…
In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…
We present a prescription in F-theory for realizing matter in "exotic" representations of product gauge groups. For 6D vacua, bifundamental hypermultiplets are engineered by starting at a singular point in moduli space which includes 6D…
We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
The goal of this article is to provide an explicit algorithmic construction of formal $F$-manifold structures, formal Frobenius manifold structures, and higher residue pairings on the primitive middle-dimensional cohomology $\mathbb{H}$ of…
In this letter we follow up recent work of Halverson-Kumar-Morrison on some exotic examples of gauged linear sigma models (GLSM's). Specifically, they describe a set of U(1) x Z_2 GLSM's with superpotentials that are quadratic in p fields,…
We present a systematic way of generating F-theory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8xE8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the…