Perturbative heterotic vacua are a highly accessible example of string models with N=1 spacetime SUSY and have seen resurgent interest recently. The role of worldsheet instantons in a nonlinear sigma model approach to these examples is crucial, yet methods for computing instanton effects are not in general known.

I report on some work on models associated to gauged linear sigma models, in which the effects of worldsheet instantons are under better control. Specializing to deformations of (2,2) models we can make some progress. Results include an extension of the (2,2) mirror map to some (0,2) deformations as well as a detailed study of the way in which the spectrum of massless singlets (first-order deformations) varies with changes in the Kahler parameters.