Wess-Zumino sigma models with non-Kahlerian geometry

TL;DR

This paper explores the geometric structures underlying supersymmetric Wess-Zumino models, revealing that relaxing action derivability leads to complex flat geometries, while enforcing it restricts models to Kahler geometry with superpotentials.

Contribution

It demonstrates how the geometry of supersymmetric models depends on whether the field equations are derivable from an action, extending understanding beyond Kahler manifolds.

Findings

Relaxed field equations lead to complex flat geometry.

Enforcing action derivability restricts models to Kahler geometry.

Superpotentials determine forces in Kahler cases.

Abstract

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.