In the context of (0, 2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality (TSD) originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has largely been studied at the level of counting states in the effective theories. We extend this analysis in several ways.

First, we consider the correspondence including the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) the detailed structure of the vacuum space of the dual theories can be explored. Our results give new evidence that GLSM target space duality may provide important hints towards a more complete understanding of (0,2) string dualities. In addition, we consider TSD theories on elliptically fibered Calabi-Yau manifolds. In this context, each half of the "dual" heterotic theories must in turn have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple K3- fibrations of the same elliptically fibered Calabi-Yau manifold. In this work we investigate this conjecture in the context of both six-dimensional and four-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. Finally, we consider Landau-Ginzburg (LG) phases of TSD theories and explore their massless spectrum. In particular, we investigate TSD pairs involving geometric singularities. We study resolutions of these singularities and their relationship to the duality.