Wess–Zumino sigma models with non-Kählerian geometry

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