Demonstrated convincingly that supergravity gives you GR

In summary, supergravity is more than just general relativity in a continuum limit. It has a larger local spacetime symmetry group and includes matter degrees of freedom. However, when supersymmetry is broken and the heavy degrees of freedom are integrated out, the classical limit yields the usual Einstein theory of gravity. The derivation of the supergravity action can be done algebraically or using the superfield formalism. The gravitational part of the action is similar to GR, but involves a Veirbein and a gravitino field. There is currently no known method to explicitly calculate the pure GR action from the supergravity action, but it can be approximated by integrating out the heavy degrees of freedom.
  • #1
hamster143
911
2
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?
 
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  • #2


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 propogating 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.
 
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  • #3


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

The derivation of classical lagrangian with [itex]R[/itex]'s and [itex]\sqrt{-g}[/itex]'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.
 
  • #4


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.
 

1. What is supergravity?

Supergravity is a theoretical framework that combines the principles of general relativity (GR) and supersymmetry (a mathematical symmetry between bosons and fermions) in order to provide a more complete understanding of gravity and the fundamental forces of nature.

2. How does supergravity relate to general relativity?

Supergravity is considered to be a supersymmetric extension of GR. This means that it incorporates the principles of GR, such as the curvature of spacetime being caused by the presence of matter and energy, while also incorporating the concept of supersymmetry to account for the behavior of particles in the quantum realm.

3. Why is it important to demonstrate that supergravity gives you GR?

Demonstrating that supergravity gives you GR is important because it provides a theoretical framework that unifies gravity with the other fundamental forces of nature, such as electromagnetism and the strong and weak nuclear forces. It also helps to bridge the gap between the classical understanding of gravity (GR) and the quantum understanding of particle behavior (supersymmetry).

4. How has it been demonstrated that supergravity gives you GR?

Supergravity has been demonstrated to give you GR through mathematical calculations and theoretical models. These have shown that the equations of supergravity can be reduced to the equations of GR in certain limits, thus providing a consistent and convincing link between the two theories.

5. What are the implications of supergravity giving you GR?

The implications of supergravity giving you GR are vast and far-reaching. It provides a more complete understanding of gravity and the fundamental forces of nature, which can potentially lead to new discoveries and advancements in physics. It also has implications for cosmology and the study of the universe on a grand scale.

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