From Rigid Supersymmetry to Twisted Holomorphic Theories

Understand

We study N=1 field theories with a U(1)_R symmetry on compact four-manifolds M.

• Supersymmetry requires M to be a complex manifold.
• The supersymmetric theory on M can be described in terms of conventional fields coupled to background supergravity, or in terms of twisted fields adapted to the complex geometry of M.
• Many properties of the theory that are difficult to see in one formulation are simpler in the other one.