Seiberg-Witten Theories on Ellipsoids

Understand

We present a set of equations for a 4D Killing spinor which guarantees the Seiberg-Witten theories on a curved background to be supersymmetric.

• The equations involve an SU(2) gauge field and some auxiliary fields in addition to the metric.
• Four-dimensional ellipsoids with U(1)xU(1) isometry are shown to admit a supersymmetry if these additional fields are chosen appropriately.
• We compute the partition function of general Seiberg-Witten theories on ellipsoids, and the result suggests a correspondence with 2D Liouville or Toda correlators with general coupling constant b.