In the book (Supergravity - Daniel Z.Freedman & Antoine Van Proeyen - Cambridge), there are (Chapters 16-17) a presentation of pure supergravity or supergravity with matter, from a SuperConformal approach.

The "simplest" link, is to begin with a Superconformal gauge multiplet coupled to a chiral multiplet, then gauge fix which will break the scale and special conformal transformation symmetries, and finally get a pure supergravity (in the same dimensional space-time). Here one speaks about $\mathcal N=1$ supersymmetry in a $D=3+1$ space-time.

I have some questions about this approach.

1) Is it only a mathematical approach, or it is also a physical approach, that is, is it possible to associate some physical quantities of the $2$ theories in some way ?

2) Thinking about AdS (4)/CFT(3), there is some regime, where supergravity is trustable. In this regime, with the above approach, we have $2$ sides of a triangle, so it may be tempting to look at the 3rd side of the triangle, that is a link between a superconformal theory in $3+1$ dimensions, with a superconformal theory in $2+1$ dimensions, or maybe a step further, that is looking at the superconformal theory in $3+1$ as a "mother" theory, as a united point of view of AdS (4)/CFT(3), at least in the supergravity regime. Does all this makes sense ?

This post imported from StackExchange Physics at 2014-03-07 13:09 (UCT), posted by SE-user Trimok