De sitter Supergravity

  • A
  • Thread starter shereen1
  • Start date
  • #1
51
1
Dear all
I just want to ask currently i am studying supergravity. Why it is much important or easier to study the AdS4 supersymmetric de Sitter group and then applying contraction to get superpoincare one than starting directly by gauging superpoincare without any contraction.
Thank you
 

Answers and Replies

  • #2
haushofer
Science Advisor
Insights Author
2,481
869
Hi Shereen,

in your former topics you asked questions without replying to answers given there, so that doesn't invite other people to try to help you. It would also help if you give some more detail, which texts you are using etc. So in the hope you will do that in the future, here a reply:

The (A)dS algebra is more general than the Poincaré algebra, so it is helpful to first gauge this algebra and obtain the resulting AdS SUGRA. From there you can always contract away the cosm.constant to obtain Poincaré-SUGRA. Something similar can be done by gauging the conformal algebra and use gauge-fixing to arrive at Poincaré-SUGRA in the context of mattercouplings.

Is this a satisfying answer?
 
  • #3
51
1
Hi Shereen,

in your former topics you asked questions without replying to answers given there, so that doesn't invite other people to try to help you. It would also help if you give some more detail, which texts you are using etc. So in the hope you will do that in the future, here a reply:

The (A)dS algebra is more general than the Poincaré algebra, so it is helpful to first gauge this algebra and obtain the resulting AdS SUGRA. From there you can always contract away the cosm.constant to obtain Poincaré-SUGRA. Something similar can be done by gauging the conformal algebra and use gauge-fixing to arrive at Poincaré-SUGRA in the context of mattercouplings.

Is this a satisfying answer?
Thank you this is so satisfying. Please can you give me a reference for gauging the conformal algebra. I have a one for micho kako
 
  • #4
haushofer
Science Advisor
Insights Author
2,481
869
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
 
  • Like
Likes shereen1
  • #5
51
1
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
Thank you i got it
 
  • #6
51
1
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
Dear Haushofer
Sorry for asking to much but your answers is so satisfying.
What is the difference between SO(2,3) and SO(1,4)?
Thank you
 
  • #7
51
1
Dear Haushofer
Sorry for asking to much but your answers is so satisfying.
What is the difference between SO(2,3) and SO(1,4)?
Thank you
sorry for the mistakes too* and are*
 
  • #8
haushofer
Science Advisor
Insights Author
2,481
869
Dear Haushofer
Sorry for asking to much but your answers is so satisfying.
What is the difference between SO(2,3) and SO(1,4)?
Thank you
SO(2,3) is the symmetrygroup of a 2+3=5-dimensional space with two timelike and 3 spacelike directions, whereas SO(1,4) is the symmetrygroup of a 1+4=5-dimensional space with one timelike and 4 spacelike directions (i.e. 5-dimensional Minkowski spacetime!).

AdS can be written as an embedding in such a "two-times spacetime". The constraint of the embedding however cuts down one timelike direction. So AdS itself does not contain two timelike directions, only the embedding space (which has no physical interpretation afaik)!

Zee's GR-book has an excellent treatment on (A)dS spaces.
 
  • Like
Likes shereen1
  • #9
51
1
SO(2,3) is the symmetrygroup of a 2+3=5-dimensional space with two timelike and 3 spacelike directions, whereas SO(1,4) is the symmetrygroup of a 1+4=5-dimensional space with one timelike and 4 spacelike directions (i.e. 5-dimensional Minkowski spacetime!).

AdS can be written as an embedding in such a "two-times spacetime". The constraint of the embedding however cuts down one timelike direction. So AdS itself does not contain two timelike directions, only the embedding space (which has no physical interpretation afaik)!

Zee's GR-book has an excellent treatment on (A)dS spaces.
Thank you i will have a look on Zee's book i have it :)
Thank you
 

Related Threads on De sitter Supergravity

  • Last Post
Replies
10
Views
1K
Replies
14
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
2K
Replies
10
Views
2K
Replies
4
Views
4K
Replies
73
Views
13K
Replies
0
Views
2K
Replies
7
Views
1K
Top