Supergravity and local symmetry

[masudr]

In chapter 4 of Bailin & Love, Supersymmetric gauge field theory and string theory, the authors state that supersymmetry is considered a global symmetry, and we can separately consider it to be a local symmetry. Further, since the supersymmetry algebra contains $P^\mu$, the generator of translations, we would also get local translation invariance, and this is a theory of gravitation, as per GR, and is called supergravity.

I just wanted to ask, that the Poincaré algebra also contains the generator of translations (of course), and if we take that to be a local symmetry, do we just get GR plain and simple? Or something else?

 

[BenTheMan]

Hopefully I understood your question. You get SUPER GR. This is what supergravity is :) That's why people were so excited about SUGRA in the 1980's. Just by assuming supersymmetry, and demanding that it be a local symmetry, you automatically get GR.

Also, check out a book by Binetruy. That is the best SUSY/SUGRA book I've found. And depending on what you want out of your reading, you can also check out Terning's book, which is largely available for free on spires. (It's more or less his 2001 TASI lectures.)

 

[blechman]

Yes! Gravity can be thought of as a "gauge theory with gauge group being the Poincare group." Furthermore, thanks to Coleman-Mandula theorem, it is unique!

BenTheMan: I think you mean John's TASI-2002 lectures (?)

 

[BenTheMan]

Err...yeah. You're right. : http://arxiv.org/abs/hep-th/0306119.

Also, depending on what you want from your SUSY studies, Peskin's TASI lectures (2006) are pretty good too, but I haven't studied them as closely: http://arxiv.org/abs/0801.1928.

 

[masudr]

Yes! Gravity can be thought of as a "gauge theory with gauge group being the Poincare group."

Is there any treatment where GR has been developed in the way we normally deal with non-Abelian gauge fields?

 

[blechman]

Is there any treatment where GR has been developed in the way we normally deal with non-Abelian gauge fields?

sure, the notion goes back to the beginnings of gauge theory. In fact, 't Hooft and Veltmann who proved renormalizability for gauge theories were actually interested in gravity, and were using gauge theories as a "warm-up" problem. Some warm-up, eh?!

A very good, but very advanced book that attacks GR in this way is Tomas Ortin's text "Gravity and Strings" - but it is quite a challenging text. The subject is very nontrivial. I do not know of any good introductions or review articles, unfortunately, but I'm sure there must be some out there. I'll leave it to other experts to make suggestions...