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I am studying formulating supergravity under De Sitter group can anyone suggest me a reference

Thank you

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- Thread starter shereen1
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- #1

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I am studying formulating supergravity under De Sitter group can anyone suggest me a reference

Thank you

- #2

jedishrfu

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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/dp/0521194016/?tag=pfamazon01-20

you can check its table of contents to see if it has what you're looking for.

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/dp/0521194016/?tag=pfamazon01-20

you can check its table of contents to see if it has what you're looking for.

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- #3

haushofer

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

- #4

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i just want tto know how can i contract from de sitter to poincareYou mean the fact that supergravity doesnt' allow for dS-vacua unless you turn on vevs?

- #5

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HelloI 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/dp/0521194016/?tag=pfamazon01-20

you can check its table of contents to see if it has what you're looking for.

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

- #6

haushofer

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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.No

i just want tto know how can i contract from de sitter to poincare

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

haushofer

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Yes, that book is great. Van Proeyen also has a lot of online notes, on which this book is based.in particular this book on Supergravity by Freedman:

https://www.amazon.com/dp/0521194016/?tag=pfamazon01-20

you can check its table of contents to see if it has what you're looking for.

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- #8

haushofer

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- #9

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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

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

- #11

haushofer

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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

[tex]

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

[/tex]

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

[tex]

[P_a,P_b ] = 0

[/tex]

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

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