From strings to the MSSM

Abstract

We review recent progress in embedding the supersymmetric standard model into string theory. We discuss how, with the incorporation of certain aspects of grand unification, a search strategy can be developed that allows to efficiently find rather large numbers of promising string vacua. Global string-derived models with the following features are discussed: (i) exact MSSM spectrum below the unification scale; (ii) R parity; (iii) hierarchical Yukawa couplings with nontrivial mixing; (iv) solution to the µ problem; (v) see-saw suppressed neutrino masses.a

Proton hexality in local grand unification

“…The picture of local grand unification has drawn considerable attention in the recent past in particular in the context of heterotic model building (for recent reviews, see [32,33]). Before discussing orbifold compactifications of the heterotic string, let us demonstrate how the previous problems are solved in a bottom-up approach with two extra dimensions 6 .…”

Three-generation asymmetric orbifold models from heterotic string theory

“…The degeneracy factor for the twisted sector is given by 15) where η i are defined as 0 ≤ t i + n i = η i < 1 for suitable integers n i . The volume of the invariant lattice is determined as Vol(I θ (Γ)) = det(g ij ) = det(α i · α j ).…”

“…Especially, in the framework of heterotic Z N or Z N × Z M orbifold compactifications [1,2], embedding a supersymmetric standard model or a higher dimensional grand unified theory into heterotic string theory is considered [3][4][5][6][7][8][9][10][11][12][13][14] (also see a review [15]). Since strings on an orbifold can be described by a solvable worldsheet conformal field theory [16,17], it is possible to calculate Yukawa couplings and selection rules [18][19][20][21][22].…”

A Z2×Z2 standard model

“…Nevertheless, such conditions might be essential to ensure that a given smooth CY compactification of supergravity has a full string lift. The VEV configuration (9) has been chosen such that the standard model group and matter parity (in particular also the hypercharge) remain unbroken. Moreover, according to table 2 in appendix A all non-empty fixed tori support twisted states to the 4D theory with VEVs switched on.…”