The moduli space of heterotic line bundle models: a case study for the tetra-quadric

Abstract

It has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of phenomenologically promising such models have been constructed for various classes of Calabi-Yau manifolds. In this paper we focus on a case study for the tetra-quadric -a Calabi-Yau hypersurface embedded in a product of four CP 1 spaces. We address the question of finiteness of the class of consistent and physically viable line bundle models constructed on this manifold. Further, for a specific semi-realistic example, we explore the embedding of the line bundle sum into the larger moduli space of non-Abelian bundles, both by means of constructing specific polystable non-Abelian bundles and by turning on VEVs in the associated low-energy theory. In this context, we explore the fate of the Higgs doublets as we move in bundle moduli space. The non-Abelian compactifications thus constructed lead to SU(5) GUT models with an additional global B−L symmetry. The non-Abelian compactifications inherit many of the appealing phenomenological features of the Abelian model, such as the absence of dimension four and dimension five operators triggering fast proton decay.

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

“…We have checked that with f restricted in this way the monad U is indeed a rank four vector bundle (rather than a sheaf) and, following the same steps as in ref. [18], we have also verified that V = U ⊕ L remains supersymmetric in the cone (4.15). To arrive at the above choice of equivariant structure we have been guided by two requirements.…”

“…In a previous publication [18], we have been led to considering such compactifications by the study of non-Abelian deformations of holomorphic line bundle sums, based on a particular example from the data base of heterotic line bundle standard models in refs. [9,10].…”

“…For the particular model, we have shown in ref. [18] that there exists a locus in moduli space where the bundle structure group generically is S (U(4) × U(1)) and the low-energy gauge group is SU(5) × U(1). The additional U(1) indeed leads to a B − L symmetry so that the model is safe from proton decay induced by dimension four operators.…”

“…This was studied in detail in ref. [18] for a generic monad map of the type (4.9) using techniques described in refs. [25,29].…”

Hodge numbers for CICYs with symmetries of order divisible by 4

“…This manifold has recently been studied in Refs. [48][49][50][51] leading to heterotic models which come very close to the desired properties of the Standard Model. The tetraquadric manifold admits 11 different smooth quotients [12].…”