We discuss singlet extensions of the MSSM with Z4R symmetry. We show that holomorphic zeros can avoid a potentially large coefficient of the term linear in the singlet. The emerging model has both an effective term and a supersymmetric mass term for the singlet N which are controlled by the gravitino mass. The term turns out to be suppressed against N by about one or two orders of magnitude. We argue that this class of models might provide us with a solution to the little hierarchy problem of the MSSM.

We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a ZM≥3R or U(1)R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the μ term. © 2011 Elsevier B.V.

N × M orbifold models admit the introduction of a discrete torsion phase. We find that models with discrete torsion have an alternative description in terms of torsionless models. More specifically, discrete torsion can be 'gauged away' by changing the shifts by lattice vectors. Similarly, a large class of the so-called generalized discrete torsion phases can be traded for changing the background fields (Wilson lines) by lattice vectors. We further observe that certain models with generalized discrete torsion are equivalent to torsionless models with the same gauge embedding but based on different compactification lattices. We also present a method of classifying heterotic N × M orbifolds. © SISSA 2007.

We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N ≥ 1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z3,Z4,Z6-I etc. and 358 with non-Abelian point groups such as S 3, D 4, A 4 etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking. © 2013 SISSA.

The well-known Giudice-Masiero mechanism explains the presence of a μ term of the order of the gravitino mass, but does not explain why the holomorphic mass term is absent in the supzerpotential. We discuss anomaly-free discrete symmetries which are both compatible with SU(5) unification of matter and the Giudice-Masiero mechanism, i.e. forbid the μ term in the superpotential while allowing the necessary Kähler potential term. We find that these are ZMR symmetries with the following properties: (i) M is a multiple of four; (ii) the Higgs bilinear H uH d transforms trivially; (iii) the superspace coordinate θ has charge M/4 and, accordingly, the superpotential has charge M/2; (iv) dimension-five proton decay operators are automatically absent. All ZMR symmetries are anomaly-free due to a non-trivial transformation of a Green-Schwarz axion, and, as a consequence, a holomorphic μ term appears at the non-perturbative level. There is a unique symmetry that is consistent with the Weinberg operator while there is a class of ZMR symmetries which explain suppressed Dirac neutrino masses. © 2012 Elsevier B.V.

We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales.

We complete our search for MSSM vacua in the Z6 - II heterotic orbifold by including models with 3 Wilson lines. We estimate the total number of inequivalent models in this orbifold to be 107. Out of these, we find almost 300 models with the exact MSSM spectrum, gauge coupling unification and a heavy top quark. Models with these features originate predominantly from local GUTs. The scale of gaugino condensation in the hidden sector is correlated with properties of the observable sector such that soft masses in the TeV range are preferred. © 2008 Elsevier B.V. All rights reserved.

We present a Z2 × Z2 orbifold compactification of the E8 × E8 heterotic string which gives rise to the exact chiral MSSM spectrum. The GUT breaking SU (5) → SU (3)C × SU (2)L × U (1)Y is realized by modding out a freely acting symmetry. This ensures precision gauge coupling unification. Further, it allows us to break the GUT group without switching on flux in hypercharge direction, such that the standard model gauge bosons can remain massless when the orbifold singularities are blown up. The model has vacuum configurations with matter parity, a large top Yukawa coupling and other phenomenologically appealing features. © 2010 Elsevier B.V. All rights reserved.

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 one 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 non-trivial mixing; (iv) solution to the μ problem; (v) see-saw suppressed neutrino masses. © 2008 Springer-Verlag / Società Italiana di Fisica.

We re-derive the R symmetries for the Z6-II orbifold with non-trivial Wilson lines and find expressions for the R charges which differ from those in the literature. © 2013 Elsevier B.V.