We discuss the possibility of light dark matter in a general singlet extension of the MSSM. Singlino LSPs with masses of a few GeV can explain the signals reported by the CRESST, CoGeNT and possibly also DAMA experiments. The interactions between singlinos and nuclei are mediated by a scalar whose properties coincide with those of the SM Higgs up to two crucial differences: the scalar has a mass of a few GeV and its interaction strengths are suppressed by a universal factor. We show that such a scalar can be consistent with current experimental constraints, and that annihilation of singlinos into such scalars in the early universe can naturally lead to a relic abundance consistent with the observed density of cold dark matter. © 2010 Elsevier B.V.

We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.

We discuss the role of approximate U(1)R symmetries for the understanding of hierarchies in Nature. Such symmetries may explain a suppressed expectation value of the superpotential and provide us with a solution to the MSSM μ problem. We present various examples in field theory and string-derived models. © SISSA 2010.

Higher-dimensional models of grand unification allow us to relate the top Yukawa coupling y t to the gauge coupling g. The tree level relation y t = g at the scale of grand unification implies, in the framework of the MSSM, a rather small ratio of Higgs expectation values tan β. We find that, in the presence of localized Fayet-Iliopoulos terms, y t is suppressed against g because the bulk fields acquire non-trivial profiles whose overlap is smaller than in the case of flat profiles. This increases the prediction for tan β to moderately large values. Thus tan β is related to the geometry of compact space. We also discuss explicit realizations of such settings in orbifold compactifications of the heterotic string. It turns out that anisotropic compactifications, allowing for an orbifold GUT interpretation, are favored. © 2009 SISSA.

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.

Recently it was shown that there is a unique Z4R symmetry for the MSSM which allows for the Yukawa couplings and dimension five neutrino mass operator, forbids the μ term and commutes with SO(10). This Z4R symmetry contains matter parity as a subgroup and forbids dimension four and five proton decay operators. We show how to construct string vacua with discrete R symmetries in general and this symmetry in particular, and present an explicit example which exhibits the exact MSSM spectrum, the Z4R symmetry as well as other desired features such as gauge-top unification. We introduce the Hilbert basis method for determining all D-flat configurations and efficient algorithms for identifying field configurations with a desired residual symmetry. These methods are used in an explicit example, in which we describe in detail how to construct a supersymmetric vacuum configuration with the phenomenologically attractive Z4R symmetry. At the perturbative level, this is a supersymmetric Minkowski vacuum in which almost all singlet fields (moduli) are fixed. © 2011 Elsevier B.V.