Philip Candelas

A three‐generation Calabi‐Yau manifold with small Hodge numbers

We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group ℤ12 and the non-Abelian dicyclic group Dic3. The quotient manifolds have χ = -6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in a toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.

Codimension-three bundle singularities in F-theory

We study new nonperturbative phenomena in N = 1 heterotic string vacua corresponding to pointlike bundle singularities in codimension three. These degenerations result in new four-dimensional infrared physics characterized by light solitonic states whose origin is explained in the dual F-theory model. We also show that such phenomena appear generically in E7→E6 higgsing and describe in detail the corresponding bundle transition.

An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts

Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fibers. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, explains much of the structure of the observed patterns.

The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding

A bstractWe construct supersymmetric compactifications of E8×E8 heterotic string theory which realise exactly the massless spectrum of the Minimal Supersymmetric Standard Model (MSSM) at low energies. The starting point is the standard embedding on a Calabi-Yau threefold which has Hodge numbers (h1,1, h2,1) = (1, 4) and fundamental group

Completing the Web of

{mathbb{Z}_{{12}}}

Z_3

, which gives an E6 grand unified theory with three net chiral generations. The gauge sym- metry is then broken to that of the standard model by a combination of discrete Wilson lines and continuous deformation of the gauge bundle. On eight distinct branches of the moduli space, we find stable bundles with appropriate cohomology groups to give exactly the massless spectrum of the MSSM.

- Quotients of Complete Intersection Calabi-Yau Manifolds

We complete the study [1] of smooth ℤ3-quotients of complete intersection Calabi-Yau threefolds by discussing the six new manifolds that admit free ℤ3 actions that were discovered in [2]. These manifolds were missed in [1] and complete the web of smooth ℤ3-quotients in a nice way. We discuss the transitions between these manifolds and include also the other manifolds of the web. This leads to the conclusion that the web of ℤ3-free quotients of complete intersection Calabi-Yau threefolds is connected by conifold transitions.

Type IIB flux vacua from G-theory II

A bstractWe construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on T4×ℂ

Calabi-Yau Threefolds With Small Hodge Numbers

{T}^4times mathbb{C}