A quadratic heterotic string field theory action is built with manifest N=1 d=4 supersymmetry, and its massless Calabi-Yau independent sector matches N=1 d=4 supergravity plus a tensor multiplet.
Siegel, Supergravity Superfields Without a Supermetric , HUTP-77/A068
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Heterotic String Field Theory with Manifest Spacetime Supersymmetry
A quadratic heterotic string field theory action is built with manifest N=1 d=4 supersymmetry, and its massless Calabi-Yau independent sector matches N=1 d=4 supergravity plus a tensor multiplet.