Heterotic T-folds with a small number of neutral moduli

TL;DR

This paper explores non-geometric heterotic string models with minimal neutral moduli, identifying classes with specific symmetry properties and proposing a new mapping to analyze their topological features.

Contribution

It systematically classifies heterotic T-fold models with few neutral moduli and introduces an inverse Gepner map for non-geometric settings.

Findings

Identified 18 inequivalent model classes with no trivial neutral moduli

Found flat directions as exactly marginal deformations

Described symmetry breaking patterns to diagonal gauge groups

Abstract

We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z_2 projections and shifts. We analyze some 2^{20} models, identifying 18 inequivalent classes and addressing variants generated by discrete torsions. They do not contain geometrical or trivial neutral moduli, apart from the dilaton. However, we show the existence of flat directions in the form of exactly marginal deformations and identify patterns of symmetry breaking where product gauge groups, realized at level one, are broken to their diagonal at higher level. We also describe an "inverse Gepner map" from Heterotic to Type II models that could be used, in certain non geometric settings, to define "effective" topological invariants.