Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations
that determine a larger class of geometries than the familiar Kahler manifolds,
in which covariantly holomorphic vectors rather than a scalar superpotential
determine the forces. Indeed, relaxing the requirement that the field equations
be derivable from an action leads to complex flat geometry. The
Batalin-Vilkovisky formalism is used to show that if one requires that the
field equations be derivable from an action, we once again recover the
restriction to Kahler geometry, with forces derived from a scalar
superpotential.Comment: 13 pages, Late