Spectra in Standard-like Z_3 Orbifold Models

TL;DR

This paper analyzes the spectra of matter states in 175 standard-like Z_3 orbifold models, identifying common patterns, hypercharge normalizations, and implications for MSSM accommodation, exotic states, and moduli stabilization.

Contribution

It provides a comprehensive classification of matter spectra patterns and hypercharge normalizations in Z_3 orbifold models, including analysis of anomalies and moduli stabilization effects.

Findings

Only 20 representation patterns occur among 175 models.

The minimal hypercharge normalization varies, sometimes below SU(5) values.

String moduli masses are close to the gravitino mass, affecting supergravity models.

Abstract

General features of the spectra of matter states in all 175 models found in a previous work by the author are discussed. Only twenty patterns of representations are found to occur. Accomodation of the Minimal Supersymmetric Standard Model (MSSM) spectrum is addressed. States beyond those contained in the MSSM and nonstandard hypercharge normalization are shown to be generic, though some models do allow for the usual hypercharge normalization found in SU(5) embeddings of the Standard Model gauge group. The minimum value of the hypercharge normalization consistent with accomodation of the MSSM is determined for each model. In some cases, the normalization can be smaller than that corresponding to an SU(5) embedding of the Standard Model gauge group, similar to what has been found in free fermionic models. Bizzare hypercharges typically occur for exotic states, allowing for matter which does not occur in the decomposition of SU(5) representations---a result which has been noted many times before in four-dimensional string models. Only one of the twenty patterns of representations, comprising seven of the 175 models, is found to be without an anomalous U(1). The sizes of nonvanishing vacuum expectation values induced by the anomalous U(1) are studied. It is found that large radius moduli stabilization may lead to the breakdown of sigma-model perturbativity. Various quantities of interest in effective supergravity model building are tabulated for the set of 175 models. In particular, it is found that string moduli masses appear to be generically quite near the gravitino mass. String scale gauge coupling unification is shown to be possible, albeit contrived, in an example model. The intermediate scales of exotic particles are estimated and the degree of fine-tuning is studied.