# A Supergravity, De Sitter

1. May 16, 2016

### shereen1

Dear all
I am studying formulating supergravity under De Sitter group can anyone suggest me a reference
Thank you

2. May 17, 2016

### Staff: Mentor

I don't have a direct answer for a book, but for those here that may it would help alot if you told us your level of education. Are you an undergrad or a graduate student in Physics?

What other physics/math courses have you taken related to Supergravity?

Lastly, you might find some references to investigate at the end of this wikipedia article:

https://en.wikipedia.org/wiki/Supergravity

in particular this book on Supergravity by Freedman:

https://www.amazon.com/Supergravity-Daniel-Z-Freedman/dp/0521194016

Last edited by a moderator: May 7, 2017
3. May 17, 2016

### haushofer

You mean the fact that supergravity doesnt' allow for dS-vacua unless you turn on vevs?

4. May 18, 2016

### shereen1

No
i just want tto know how can i contract from de sitter to poincare

5. May 18, 2016

### shereen1

Hello
I took a course on supersymmetry and supergravity in addition to a graduate course on mathematical physics.

6. May 20, 2016

### haushofer

You mean a Inönü-Wigner contraction in the underlying algebra? You take the radius of curvature R and send it to infinity, R --> oo. I'm not sure if you also can do this contraction straight away in the transformation rules and the curvatures; one has to be careful with this, but you can check that immediately for yourself.

You are aware of the 'problematic' relation between deSitter and SUGRA? E.g., have you tried (and failed :P ) to write down pure D=4,N=1 SUGRA on an AdS background?

7. May 20, 2016

### haushofer

Last edited by a moderator: May 7, 2017
8. May 20, 2016

### haushofer

Shereen1, if you want serious answers with content here you should formule questions with content; at least some background. I responded to your question about torsion in SUGRA earlier, but it's not very stimulating if you don't reply to your questions or give no context. 'Contraction" can mean a lot of things. And what kind of SUGRA are you studying? What references did you find so far? Which textbook? Etc.

9. May 20, 2016

### shereen1

Dear Haushofer
In fact i am using notes written by my professor. In addition to P. van Nieuwenhuizen book (Supergravity).
I will have a look on Freedman and Van Proyen book
Thank you

10. May 20, 2016

### shereen1

I will start doing the contraction. In fact i didnt start yet dealing with AdS Backgrounds.

11. May 20, 2016

### haushofer

Ok. I'm not sure how well-suited Van Nieuwenhuizen's book is for a first exposure, but that's up to you to decide :P I really like Henning Samtleben's notes; they are (afaik) by far the most approachable first exposure to SUGRA you can think of.

The contraction in the algebra is quite easy; if you rewrite the (A)dS algebra in terms of translations P and Lorentz transformations M, then schematically, the radius of curvature R appears in the commutator

$$[P_a, P_b ] \sim \pm\frac{1}{R^2} M_{ab}$$

where the plus/minus depends on your convention, giving dS or AdS. Sending R to infinity simply gives

$$[P_a,P_b ] = 0$$

which is the well-known result of the Poincare algebra that translations commute because spacetime is flat.