Double copy and complex scalar manifolds in N=2 supergravity

Scalar fields in supersymmetric gravitiational theories (i.e. supergravity theories) are constrained to span complex manifolds with very special properties. The metrics of such scalar manifolds make an imprint on scattering amplitudes of supergravity, which are notoriously hard to calculate using conventional methods such as Feynman diagrams. A more convenient method which can be used for many supergravities is the so-called 'double copy' construction. Double copy is a way to produce supergravity scattering amplitudes by applying some simple operations to the scattering amplitudes of the corresponding gauge theories, which are much easier to calculate. In this talk, we will describe double copy constructions for 4d supergravities with N=2 supersymmetries at tree-level and discuss scalar metrics that arise in such double copies. We will also briefly discuss the effect of the loop corrections in gauge theories on the corresponding scalar metrics in N=2 supergravities.