Anti de Sitter space and black hole information

[lark]

So a string theory with gravity in anti de Sitter space apparently resolves the black hole information paradox via the adS/CFT correspondence.
I'm wondering: is the anti de Sitter space somehow necessary to string theory with gravity? Or is it just because there's this adS/CFT correspondence.
Also, this anti de Sitter space is 5-dimensional, I think.
The universe is expanding and cosmological spacetime looks like de Sitter space right now, I guess.
Can that 5-D anti de Sitter space be combined with de Sitter space? So that locally it would look like anti de Sitter space and on a large scale like de Sitter space?
thanks
Laura

 

[AndyW]

Dear Laura,

Thank you for your inquiry about string theory and the anti de Sitter (adS) space. To answer your question, the adS space is indeed necessary for string theory with gravity. This is because the adS space allows for a consistent way to incorporate gravity into the framework of string theory. In other words, the adS space provides a mathematical framework that allows for the unification of gravity and quantum mechanics, which is one of the main goals of string theory.

The adS/CFT correspondence is a powerful tool that allows for the study of quantum gravity in the adS space. This correspondence states that there is a duality between theories in the adS space and conformal field theories (CFTs) on the boundary of the adS space. This duality has been proven in many cases and has led to significant progress in our understanding of quantum gravity.

As for the dimensions of the adS space, it is indeed 5-dimensional. This is because string theory requires 10 dimensions in order to be consistent, and the adS space is a special case where 5 of those dimensions are compactified. This means that they are curled up and not observable in our 4-dimensional world. The remaining 5 dimensions of the adS space are what allow for the incorporation of gravity into string theory.

Regarding the combination of adS and de Sitter (dS) space, it is possible to have a spacetime that locally appears adS while on a larger scale appears dS. This is known as the "adS/dS spacetime" and has been studied in the context of cosmology. However, it should be noted that this is still an area of active research and there is no definitive answer on the nature of this spacetime.

I hope this helps to answer your questions about the adS space and its role in string theory with gravity. If you have any further inquiries, please do not hesitate to ask.