On heterotic model constraints

TL;DR

This paper examines the constraints on heterotic string compactifications, demonstrating that relaxing these constraints leads mostly to inconsistent or non-viable models, with only one known globally consistent supersymmetric example.

Contribution

The authors show that weakening heterotic model constraints results in mostly frivolous models, and they explore modifications to known solutions to achieve perturbative, stable configurations.

Findings

Most relaxed models are inconsistent or anomalous.

Only one model remains globally consistent and supersymmetric.

Many additional solutions are found but lack global consistency.

Abstract

The constraints imposed on heterotic compactifications by global consistency and phenomenology seem to be very finely balanced. We show that weakening these constraints, as was proposed in some recent works, is likely to lead to frivolous results. In particular, we construct an infinite set of such frivolous models having precisely the massless spectrum of the MSSM and other quasi-realistic features. Only one model in this infinite collection (the one constructed in arXiv:hep-th/0512149) is globally consistent and supersymmetric. The others might be interpreted as being anomalous, or as non-supersymmetric models, or as local models that cannot be embedded in a global one. We also show that the strongly coupled model of arXiv:hep-th/0512149 can be modified to a perturbative solution with stable SU(4) or SU(5) bundles in the hidden sector. We finally propose a detailed exploration of heterotic vacua involving bundles on Calabi-Yau threefolds with Z_6 Wilson lines; we obtain many more frivolous solutions, but none that are globally consistent and supersymmetric at the string scale.