Why should N=8 Supergravity be finite?

Why should N=8 Supergravity be finite?

I would like to attempt to explain here why adding N=8 supersymmetry to General Relativity should have the chance of making the theory finite.

Firstly, it is known that the only renormalizable theories are those of spin 0, spin 1/2 and spin 1 particles.  General Relativity, however, is quantized by spin 2 particles - gravitons. (Adding simple N=1 supersymmetry to GR also adds spin 3/2 particles - gravitinos).

If we add N=8 supersymmetry we have a single super-particle whose components compose of spin 2, 3/2, 1, 1/2, 0 , -1/2, -3/2, -2 particles. We can think of this as some kind of super-vector. There are (1,8,28,56,72,56,28,8,1) of each of these types of particles respectively.

What we would like to do is get rid of these spin 2 and spin 3/2 components (18 of them) because they are non-renormalizable. So, we should like to be able to rotate this super-vector in such a way that these components become zero. We also, need to rotate this super-vector a different amount at every point in space-time. i.e. it needs to be a local transformation.

But, N=8 Supergravity has this very capacity in that it is invariant under local supersymmetry transformations! The question is, is there enough freedom to always set 18 components of the super-vector to zero? Also, in any Feynman diagram can we rotate the virtual propagators so that they don't depend on these 18 non-renormalizable components? These are very tricky details, and it has not been proved that this is possible, but we see that N=8 supersymmetry can definitely help making GR behave better.

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