Demonstrated convincingly that supergravity gives you GR

[hamster143]

Has it ever been demonstrated convincingly that supergravity gives you GR in the continuum limit (as opposed to just some massless spin-2 field)?

Where can I find a readable derivation of this fact?

 

[Haelfix]

What do you mean by 'GR' exactly? The exact equations of motion?

Supergravity is more than GR in a sense, and depending on how you arrange things its not necessarily trivial to decouple them. The local spacetime symmetry group is enhanced and there are unavoidable matter d.o.f propagating around (in a sense they have to be there, and aren't put in by hand).

However, in the limit where supersymmetry is broken and the heavy degrees of freedom are integrated out or moved over into the matter portion of the lagrangian, than yea you can get the usual Einstein theory of gravity in the classical limit.

 

[hamster143]

What do you mean by 'GR' exactly? The exact equations of motion?

The derivation of classical lagrangian with $R$'s and $\sqrt{-g}$'s would suffice.

Somehow by examining relevant chapters in e.g. Weinberg, I get the impression that all we really get is linearised gravity instead.

 

[Haelfix]

Blah, I just had a long reply eaten. Paraphrasing quickly

How you actually derive the supergravity action is usually done by linearizing and working algebraically, as opposed to using the superfield formalism (although it can be done).

However once you actually have found it, you can simply take the sugra action at face value and nothing needs to be linearized a priori, it just turns out that it is convenient for some purposes.

Further, the gravitational part of the SUGRA action is remarkably similar to the usual GR action. The subtleties is that instead of having only one metric field at play, here you have a Veirbein, and a gravitino field (+ maybe an auxiliary field if you don't want to use the eom). The curvature R is also calculated with a spin connection (since we have fermions in the theory).

Anyway, what you want to show is how to get pure GR from this action. Well the problem really is how you go about breaking supersymmetry, since that is an unknown mechanism.

I don't know of a reference where its calculated explicitly (there is no obvious Inonu-Wigner like contraction method that is possible afaik), but you can handwave a lot of it through yourself by simply brute force taking the effective field theory after integrating out all the heavy d.o.f.