Spectra in Standard-like Z3 Orbifold 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 σ-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.

Higgs mechanism in heterotic orbifolds

“…Since a detailed discussion on how to do this can be found in the literature (e.g. [22,50]) we refrain from the presentation of the relevant calculation. The 27 can be obtained by multiplying the first three entries of the root vectors appearing in the 27 with −1 (reversing the (H 1 , K, L) charges).…”

More modular invariant anomalous U(1) breaking

“…A related issue, that will also be taken up in [19], is the stabilization of the dilaton ℓ in the presence of matter fields with large vev's. In [2] it was noted that all models in the class studied there suffer from a Tmoduli mass problem. Stabilization of the T-moduli through an effective theory of gaugino condensation will allow us to address how the moduli masses may change in the presence of a U(1) X factor; indeed, we will show that the mass is modified and that this may ameliorate the moduli problem discussed in [2].…”

“…2 The only effect of the term linear in Σ ′ is a slight modification of the Kähler potential for the moduli:…”

“…We start with the effective theory at the string scale defined as in [1]: 2) whereL is the real superfield functional For reasons explained in [1], we are not using U(1) K superspace for the Abelian gauge groups that are broken at the string scale by the anomalous U(1) X . Since the underlying theory is anomaly free, it is known [4] that the apparent anomaly is canceled by a four-dimensional version of the Green-Schwarz (GS) mechanism [5].…”

Twenty-five questions for string theorists

“…The anomalous U(1) is a prime example, and models have been constructed where the massive gauge bosons of this anomalous U(1) play a role in transmitting SUSY breaking to the observable sector [63,64]. Furthermore, states which are bi-fundamental under a subgroup of the Standard Model and under a hidden sector group have been shown to be present in bosonic heterotic string constrictions [65,66], free-fermionic constructions [67], Type IIA constructions [54] and others.…”