Prepotentials for (2,2) Supergravity
  We present a complete solution of the constraints for two-dimensional, N=2 supergravity in N=2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield $H^m$ and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield $\phi$. 
Marcus T. Grisaru and Marcia E. Wehlau