Semirigid Supergravity

We formulate two-dimensional topological gravity starting from local N = 2 superconformal geometry. The theory is free from the very beginning. The usual ‘‘twisting’’ of the N = 2 algebra emerges from symmetry breaking when we expand about a nonzero value for one of the ghost fields. The mysterious linear term in the supercurrent emerges automatically, as does a full superfield formalism for the whole system including ghosts. We analyze the moduli space of the ‘‘semirigid’’ super Riemann surfaces associated with this theory, including their allowed degenerations.