I've been reading this paper http://arxiv.org/abs/hep-th/0110263. In section 4, he discusses the benefits of writing the supergravity action in a superconformal way. I have a few questions regarding this:
Why is (4.1) "superconformal"? I'm not sure I see how it is invariant under either conformal or SUSY transformations?
Why in the second line of (4.1) is he all of a sudden talking about dilatation symmetry? Is it a general feature of superconformal actions that you pick up an extra dilatation symmetry?
Assuming my previous point is correct and that the extra symmetry we pick up when going to a superconformal description is a dilatation symmetry, I still don't see what use this is? What do we gain by doing this? How is it helpful?