Andrei Constantin

A Comprehensive Scan for Heterotic SU(5) GUT models

A bstractCompactifications of heterotic theories on smooth Calabi-Yau manifolds remain one of the most promising approaches to string phenomenology. In two previous papers, arXiv:1106.4804 and arXiv:1202.1757, large classes of such vacua were constructed, using sums of line bundles over complete intersection Calabi-Yau manifolds in products of projective spaces that admit smooth quotients by finite groups. A total of 1012 different vector bundles were investigated which led to 202 SU(5) Grand Unified Theory (GUT) models. With the addition of Wilson lines, these in turn led, by a conservative counting, to 2122 heterotic standard models. In the present paper, we extend the scope of this programme and perform an exhaustive scan over the same class of models. A total of 1040 vector bundles are analysed leading to 35, 000 SU(5) GUT models. All of these compactifications have the right field content to induce low-energy models with the matter spectrum of the supersymmetric standard model, with no exotics of any kind. The detailed analysis of the resulting vast number of heterotic standard models is a substantial and ongoing task in computational algebraic geometry.

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.

Completing the Web of

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.

Z_3

We study heterotic Calabi-Yau models with hypercharge flux breaking, where the visible E-8 gauge group is directly broken to the standard model group by a nonflat gauge bundle, rather than by a two-step process involving an intermediate grand unified theory and a Wilson line. It is shown that the required alternative E-8 embeddings of hypercharge, normalized as required for gauge unification, can be found and we classify these possibilities. However, for all but one of these embeddings we prove a general no-go theorem which asserts that no suitable geometry and vector bundle leading to a standard model spectrum can be found. Intuitively, this happens due to the large number of index conditions which have to be imposed in order to obtain a correct physical spectrum in the absence of an underlying grand unified theory.

- Quotients of Complete Intersection Calabi-Yau Manifolds

A bstractWe consider heterotic Calabi-Yau compactifications with S(U(4) × U(1)) background gauge fields. These models lead to gauge groups with an additional U(1) factor which, under certain conditions, can combine with hypercharge to a B − L symmetry. The associated gauge boson is automatically super-massive and, hence, does not constitute a phenomenological problem. We illustrate this class of compactifications with a model based on the monad construction, which leads to a supersymmetric standard model with three families of quarks and leptons, one pair of Higgs doublets, three right-handed neutrinos and no exotics charged under the standard model group. The presence of the B − L symmetry means that the model is safe from proton decay induced by dimension four operators. Due to the presence of a special locus in moduli space where the bundle structure group is Abelian and the low-energy symmetry enhances we can also show the absence of dimension five proton-decay inducing operators.

Hypercharge Flux in Heterotic Compactifications

A bstractWe present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification [1].

A heterotic standard model with B − L symmetry and a stable proton

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

Type IIB flux vacua from G-theory II

{T}^4\times \mathbb{C}