Covariant N ≤ 2 heterotic string in four dimensions

We construct a covariant formulation of the heterotic superstring on K3 × T² with manifest N ≤ 2 supersymmetry. We show how projective superspace appears naturally in the hybrid formulation giving a (partially) geometric interpretation of the harmonic parameter. The low-energy effective action for this theory is given by a non-standard form of N ≤ 2 supergravity which is intimately related to the N ≤ 1 old-minimal formulation. This formalism can be used to derive new descriptions of interacting projective superspace field theories using Berkovits' open string field theory and the heterotic Berkovits-Okawa-Zwiebach construction.