Voisin-Borcea manifolds and heterotic orbifold models

Abstract

Abstract:We study the relation between a heterotic T 6 /Z 6 orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a Z 2 quotient of T 4 /Z 3 × T 2 . We consider a two-step resolution, whose intermediate step is (K3 × T 2 )/Z 2 . This allows us to identify the massless twisted states which correspond to the geometric Kähler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after higgsing does not even include the standard model gauge group. Moreover, after higgsing, the massless spectrum is non-chiral under the surviving gauge group.

Schoen manifold with line bundles as resolved magnetized orbifolds

“…When this involution has been modded out the resulting geometry corresponds to the DW(1-3) orbifold with Hodge numbers (11,11) in the classification [29]. In order that this is a symmetry of the full model, the discrete Wilson lines get severely restricted, i.e.…”

“…Therefore, this partial blow-down leads to an intermediate T 4 / 2 orbifold with torus coordinates (z 2 , z 3 ) on which the 2 action acts via the twist v θ given in (3) (c.f. [11]).…”

“…Unfortunately, an exact string quantization is out of reach at a generic point in moduli space and there is typically much less symmetry. For example, it turns out that in full blow-up any mini-landscape model has broken hypercharge [10,11]. This might be interpreted in two ways: Either one does not go to the full blow-up in order to keep hypercharge unbroken and our string vacuum is very close to the orbifold point, or our string vacuum is at a generic point of the moduli space and different constructions are needed for phenomenology.…”

Heterotic mini-landscape in blow-up

“…In describing the departure from the orbifold point within realistic compact orbifolds [39,43,44] some difficulties were encountered in the Z 6II Mini-Landscape [1,17,45] 1 and the Z 2 × Z 2 Blaszczyk model of [47]. The problems have two sources.…”

6D effective action of heterotic compactification on K3 with nontrivial gauge bundles

“…in blown-up orbifolds or more generally in smooth Calabi-Yau backgrounds. The relation between orbifold and smooth Calabi-Yau compactifications is addressed in [13][14][15][16][17][18][19][20]. In this paper we focus instead on the 6D intermediate theory and derive the effective action for smooth K3 compactifications from a Kaluza-Klein reduction.…”