Formulating Supergravity Under De Sitter Group: A Comprehensive Reference

In summary: This is why you can't have a dS-vacuum in supergravity, unless you turn on vevs.)In summary, this student is studying formulating supergravity under De Sitter group and is looking for a reference. He has taken courses in supersymmetry and supergravity, is aware of the 'problematic' relation between deSitter and SUGRA, and is looking for a book on the subject.
  • #1
shereen1
51
1
Dear all
I am studying formulating supergravity under De Sitter group can anyone suggest me a reference
Thank you
 
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  • #2
I don't have a direct answer for a book, but for those here that may it would help a lot 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.
 
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  • #3
You mean the fact that supergravity doesnt' allow for dS-vacua unless you turn on vevs?
 
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  • #4
No
haushofer said:
You mean the fact that supergravity doesnt' allow for dS-vacua unless you turn on vevs?
i just want tto know how can i contract from de sitter to poincare
 
  • #5
jedishrfu said:
I don't have a direct answer for a book, but for those here that may it would help a lot 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.
Hello
I took a course on supersymmetry and supergravity in addition to a graduate course on mathematical physics.
 
  • #6
shereen1 said:
No

i just want tto know how can i contract from de sitter to poincare
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?
 
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  • #7
jedishrfu said:
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.
Yes, that book is great. Van Proeyen also has a lot of online notes, on which this book is based.
 
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  • #8
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.
 
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  • #9
haushofer said:
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.
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
haushofer said:
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?
I will start doing the contraction. In fact i didnt start yet dealing with AdS Backgrounds.
 
  • #11
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

[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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1. What is supergravity?

Supergravity is a theory that combines the principles of general relativity and supersymmetry to describe the interactions of gravity with other fundamental forces in the universe. It is a proposed extension of Einstein's theory of general relativity, which only considers the gravitational force.

2. What is the De Sitter group?

The De Sitter group is a mathematical group that describes the symmetries of a spacetime with a positive cosmological constant. It is named after the Belgian mathematician Willem de Sitter and is one of the three possible isometry groups of a maximally symmetric spacetime, along with the Poincaré group and the anti-de Sitter group.

3. Why is formulating supergravity under the De Sitter group important?

Formulating supergravity under the De Sitter group is important because it allows for a more complete understanding of the universe by incorporating both gravity and supersymmetry. It also has implications for cosmology, as the De Sitter group is related to the expansion of the universe and the presence of dark energy.

4. What does the comprehensive reference cover?

The comprehensive reference covers the development and formulation of supergravity under the De Sitter group, including its mathematical foundations and applications to cosmology and particle physics. It also includes discussions on its current status and potential future developments in the field.

5. Who can benefit from reading this reference?

Scientists, researchers, and graduate students in the fields of theoretical physics, cosmology, and particle physics can benefit from reading this reference. It can also be a valuable resource for those interested in the development and applications of supergravity under the De Sitter group.

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