Localization on round sphere revisited

Understand

We consider supersymmetric gauge theories on round 3-sphere with a certain background gauge field.

• The Lagrangians break the usual symmetry because the background gauge field which we have turned on violates the isometry.
• In order to maintain the supersymmetry, we choose unfamiliar charged Killing spinors as N = 2 SUSY parameters.
• We perform localization calculous within this setup and find the double sine function as we expected.