Exploring Curved Superspace (II)

Understand

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry.

• With one exception, we find that M must be a Hermitian manifold.
• However, the presence of supersymmetry imposes additional restrictions.
• For instance, a supercharge that squares to zero exists, if the canonical bundle of the Hermitian manifold M admits a nowhere vanishing, holomorphic section.