# De sitter Supergravity

• A
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

haushofer
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.

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.

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

haushofer
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.

shereen1
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
Thank you i got it

Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
Dear Haushofer
What is the difference between SO(2,3) and SO(1,4)?
Thank you

Dear Haushofer
What is the difference between SO(2,3) and SO(1,4)?
Thank you
sorry for the mistakes too* and are*

haushofer
Dear Haushofer
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.

shereen1
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