This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them.

Resolutions of certain toroidal orbifolds, like T6/Z2xZ2, are far from unique, due to triangulation dependence of their resolved local singularities. This leads to an explosion of the number of topologically distinct smooth geometries associated to a single orbifold. By introducing a parameterisation …

Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher’s gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non–Lorentz invariant gauge fixing. A left–over of the gauge symmetry can be used to removed …

In this review we describe the recent progress in understanding of field theory on singular orbifolds and compare some of these results with corresponding string computations. Using orbifold trace formulae expressions for anomalies and tadpoles are obtained. For more complicated computations like the …

Supersymmetric non-linear unification in particle physics: Kähler manifolds, bundles for matter representations and anomaly cancellation.