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.

Models with modular flavor symmetries have been thought to be highly predictive. We point out that these predictions are subject to corrections from non–holomorphic terms in the Lagrangean. Specifically, in the models discussed in the literature, the Kähler potential is not fixed by the symmetries, for instance. The most general Kähler potential consistent with the symmetries of the model contains additional terms with additional parameters, which reduce the predictive power of these constructions. We also comment on potential ways of how one may conceivably retain the predictivity.

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 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.

We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the so-called 'anomalous' U(1). © 2008 Elsevier B.V. All rights reserved.

We study the possibility of realizing the neutrino seesaw mechanism in the E(8) x E(8) heterotic string. In particular, we consider its Z6 orbifold compactifications leading to the supersymmetric standard model gauge group and matter content. We find that these models possess all the necessary ingredients for the seesaw mechanism, including the required Dirac Yukawa couplings and large Majorana mass terms. We argue that this situation is quite common in heterotic orbifolds. In contrast with the conventional seesaw of grand unified theories (GUTs), no large GUT representations are needed to generate the Majorana mass terms. The total number of right-handed neutrinos can be very large, up to O(100).

Nontrivial strong dynamics often leads to the appearance of chiral composites. In phenomenological applications, these can either play the role of Standard Model particles or lift chiral exotics by partnering with them in mass terms. As a consequence, the RG flow may change the effective number of chiral generations, a phenomenon we call generation flow. We provide explicit constructions of globally consistent string models exhibiting generation flow. Since such constructions were misclassified in the traditional model searches, our results imply that more care than usually appreciated has to be taken when scanning string compactifications for realistic models.

Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional parameters, which limit the predictive power of this scheme. In this work, we introduce the scheme of quasi–eclectic flavor symmetries as a simple fix. These symmetries are the direct product of a modular and a traditional flavor symmetry, which are spontaneously broken to a diagonal modular flavor subgroup. This allows us to construct a version of Feruglio's model with the Kähler terms under control. At the same time, the starting point is reminiscent of what one obtains from explicit string models.