The Geometry of Supersymmetric Partition Functions

Understand

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M.

• Our primary focus is the dependence of Z_M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries.
• For N=1 theories with a U(1)_R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric.
• We find that Z_M is independent of the metric and depends holomorphically on the complex structure moduli.