Extended Supersymmetry on Curved Spaces

Understand

We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization.

• The conditions for supersymmetry are equivalent to a set of differential constraints including a "generalised" conformal Killing spinor equation depending on various background fields.
• We solve these equations in the general case and give very explicit expressions for the auxiliary fields that we need to turn on to preserve some supersymmetry.
• As opposed to what has been observed for the N=1 case, the conditions for unbroken supersymmetry turn out to be almost independent of the signature of spacetime, with the exception of few degenerate cases including the topological twist.