Exploring Curved Superspace

Understand

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry.

• We find that M admits a single supercharge, if and only if it is a Hermitian manifold.
• The supercharge transforms as a scalar on M.
• We then consider the restrictions imposed by the presence of additional supercharges.