Superspace formulations of ten-dimensional supergravity
  We present a new formulation for N=1, D=10 supergravity in superspace, in presence of a Lorentz Chern-Simons-form. This formulation entails the following properties: it furnishes a solution of the Bianchi identities that is algebraically consistent to all orders in alpha'; at first order it is the simplest formulation proposed so far, and it is therefore most suitable for an explicit higher order analysis; it allows a well defined perturbative expansion in alpha', in which no poltergeist fields appear; it reconciles the two different classes of first order solutions available in the literature, that until now appeared physically inequivalent. 
Kurt Lechner, Mario Tonin