Conformal field theories with higher spin currents have been known to govern type II string dynamics in exceptional holonomy manifolds since the work of Shatashvili and Vafa. From a nonlinear sigma-model viewpoint, the reduction of holonomy yields chiral symmetries extending (1,1) supersymmetry. I will generalise this result to generic (1,0) models with Fermi superfields, appropriate in particular for heterotic compactifications. I will then comment on anomalies of these symmetries, as a first step to bridge the gap between target space geometry and abstract conformal field theory. Based on work to appear shortly, joint with Xenia de la Ossa.