The MSSM spectrum from (0,2)-deformations of the heterotic standard embedding

Abstract

We construct supersymmetric compactifications of E 8 ×E 8 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 (h 1,1 , h 2,1 ) = (1, 4) and fundamental group Z 12 , which gives an E 6 grand unified theory with three net chiral generations. The gauge symmetry 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.

Heterotic line bundle standard models

“…[35] were essentially constructed at the "upstairs" GUT level. The structure group of the bundle V on the Calabi-Yau manifolds X was chosen to be S(U(1) 5 ) ⊂ E 8 so that the low-energy gauge group is SU(5) × S(U(1) 5 ), with the additional U(1) symmetries being Green-Schwarz anomalous (and hence, spontaneously broken) in most cases. The GUT matter spectrum for all models consists of 3|Γ| 10 and5 multiplets, some number of 5-5 vector-like pairs and a number of SU (5) singlets.…”

“…5 Given these expressions for the D-terms, we can now interpret the geometric discussion above from a four-dimensional point of view.…”

“…In essence, this leaves the heterotic string, F-theory and the lesser studied G 2 compactifications of M-theory as primary starting points for string phenomenology. Traditionally, heterotic Calabi-Yau model building has been based on the standard embedding [3][4][5] whereby the Bianchi identity is solved by setting the internal gauge bundle V equal to the tangent bundle, T X, of the Calabi-Yau manifolds X. However, over the past decade it has been realized that this approach is too restrictive and the focus has shifted to the wider class of non-standard embedding models [6]- [18], where V is a more general bundle over X.…”

“…However, over the past decade it has been realized that this approach is too restrictive and the focus has shifted to the wider class of non-standard embedding models [6]- [18], where V is a more general bundle over X. Only a relatively small number of models exhibiting a realistic massless spectrum have been constructed in this way, some with [6] and some without [5,11,18] antibranes, reflecting the considerable technical problems associated with vector bundles on smooth Calabi-Yau manifolds. They are complemented by models found in related heterotic constructions such as those based on orbifolds [19][20][21][22][23][24][25][26][27][28], on the free fermionic strings [29][30][31], and on Gepner models [32][33][34].…”

Classification of symmetric toroidal orbifolds

“…In most of the models discussed so far, the larger symmetry gets broken locally at some fixed point. Yet it has been argued that 'non-local' GUT symmetry breaking, as utilized in the context of smooth compactifications of the heterotic string [40][41][42][43], has certain phenomenological advantages [44,45]. Explicit MSSM candidate models, based on the DW classification, featuring non-local GUT breaking have been constructed recently [28,29].…”