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.
Construction of action for heterotic string field theory including the Ramond sector
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Extending the formulation for open superstring field theory given in arXiv:1508.00366, we attempt to construct a complete action for heterotic string field theory. The action is non-polynomial in the Ramond string field Psi, and we construct it order by order in Psi. Using a dual formulation in which the role of eta and Q is exchanged, the action is explicitly obtained at the quadratic and quartic order in Psi with the gauge transformations.
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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.