Study "De Sitter Supergravity" Effectively

In summary: Zee's book i have it :)In summary, the conversation discusses the importance of studying the AdS4 supersymmetric de Sitter group and the use of contraction to obtain superpoincare, as well as the difference between SO(2,3) and SO(1,4). A suggested reference for gauging the conformal algebra is Van Proeyen's lecture notes on sugra or his book with Freedman. The book "GR" by Zee is recommended for further understanding of (A)dS spaces.
  • #1
shereen1
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
 
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  • #2
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
haushofer said:
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
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
 
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  • #5
haushofer said:
Van Proeyen's lecture notes on sugra or his book with Freedman contain all the details.
Thank you i got it
 
  • #6
haushofer said:
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
shereen1 said:
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
shereen1 said:
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.
 
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  • #9
haushofer said:
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
 

What is "De Sitter Supergravity" and why is it important to study?

"De Sitter Supergravity" is a theoretical framework in physics that combines the principles of supersymmetry and general relativity to describe the behavior of particles in a universe with a positive cosmological constant. It is important to study because it has the potential to explain the accelerated expansion of the universe and address outstanding questions in cosmology and particle physics.

What are the main challenges in studying "De Sitter Supergravity"?

One of the main challenges in studying "De Sitter Supergravity" is its complexity, as it involves advanced mathematical concepts and requires a deep understanding of both supersymmetry and general relativity. Another challenge is the lack of experimental evidence to support its predictions, making it a purely theoretical concept at this point.

What are the current research areas in "De Sitter Supergravity"?

Current research in "De Sitter Supergravity" focuses on developing new mathematical techniques and models to better understand its properties and potentially make testable predictions. Other areas of interest include studying its implications for cosmology and its connections to other areas of physics, such as string theory.

What are the potential applications of "De Sitter Supergravity"?

The potential applications of "De Sitter Supergravity" are wide-ranging and include advancements in our understanding of the fundamental laws of nature, potential solutions to the dark energy problem, and insights into the early universe. It may also have practical applications in fields such as quantum computing and high-energy physics.

What is the role of collaboration in studying "De Sitter Supergravity"?

Collaboration plays a crucial role in studying "De Sitter Supergravity" as it involves a diverse range of expertise and perspectives. Collaborative efforts between theoretical physicists, mathematicians, and experimentalists are necessary to make progress in this complex and challenging field of study.

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