Wess–Zumino sigma models with non-K?hlerian geometry

Supersymmetry of the Wess–Zumino (N = 1, D = 4) multiplet allows field equations that determine a larger class of geometries than the familiar K?hler 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 K?hler geometry, with forces derived from a scalar superpotential.