Top quark mass coupling and classification of weakly-coupled heterotic superstring vacua

The quest for the Standard Model among the huge number of string vacua is usually based on a set of phenomenological criteria related to the massless spectrum of string models. In this work we study criteria associated with interactions in the effective low energy theory and in particular with the presence of the coupling that provides mass to the top quark. Working in the context of the Free Fermionic Formulation of the heterotic superstring, we demonstrate that, in a big class of phenomenologically promising $Z_2\times Z_2$ compactifications, these criteria can be expressed entirely in terms of the generalised GSO projection coefficients entering the definition of the models. They are shown to be very efficient in identifying phenomenologically viable vacua, especially in the framework of computer-based search, as they are met by approximately one every $10^4$ models. We apply our results in the investigation of a class of supersymmetric Pati-Salam vacua, comprising $10^{16}$ configurations, and show that when combined with other phenomenological requirements they lead to a relatively small set of about $10^7$ Standard Model compatible models that can be fully classified.Comment: 13 pages, 1 figure, minor changes, to be published in The European Physical Journal

The "landscape" of Pati--Salam heterotic superstring vacua

The main aspects of a recently developed method for classification of heterotic superstring vacua in the Free Fermionic Formulation are presented. Using these techniques we classify a big number of approximately $10^{15}$ heterotic string vacua with Pati--Salam, SU(4)x{SU(2)}_Lx{SU(2)}_R gauge symmetry with respect to their main phenomenological features as the number of families, Pati--Salam breaking Higgs, Standard Model Higgs doublets, additional triplets and exotic charge states. We identify an interesting subclass of these vacua, approximately one to one million, whose massless spectrum is completely free of fractionally charge states.Comment: 4 pages, 2 figues, Presented at "School and Workshops on Cosmology and Strings: Theory-Cosmology-Phenomenology" (CORFU2009), September 6-13, Corfu, Greec

Nonequational Stable Groups

We introduce a combinatorial criterion for verifying whether a formula is not the conjunction of an equation and a co-equation. Using this, we give a transparent proof for the nonequationality of the free group, which was originally proved by Sela. Furthermore, we extend this result to arbitrary free products of groups (except $\mathbb{Z}_2*\mathbb{Z}_2$), providing an abundance of new stable nonequational theories.Comment: 10 pages, 1 figur

A Solution to the Decompactification Problem in Chiral Heterotic Strings

We present a solution to the decompactification problem of gauge thresholds in chiral heterotic string theories with two large extra dimensions, where supersymmetry is spontaneously broken by the Scherk-Schwarz mechanism. Whenever the Kaluza-Klein scale is much lower than the string scale, the infinite towers of heavy states contribute non-trivially to the renormalisation of gauge couplings, which typically grow linearly with the large volume of the internal space and invalidate perturbation theory. We trace the origin of the decompactification problem to properties of the six dimensional theory obtained in the infinite volume limit and show that thresholds may instead exhibit logarithmic volume dependence and we provide the conditions for this to occur. We illustrate this mechanism with explicit string constructions where the decompactification problem does not occur.Comment: 26 pages, 1 figur