Horizon in AdS/CFT: CFT in Black Hole Spacetime

In summary: This results in a mixed state where each CFT has a tiny bit of information about the other, but they're unable to combine their information to form a complete picture.
  • #1
atyy
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In a spacetime with a black hole, where is the horizon in the CFT?

Also, if a black hole spacetime corresponds to a thermal CFT, doesn't that mean the CFT is in a box where there is still a universe outside to provide a temperature?
 
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  • #2
Hmm, here there are two copies of the CFT and one of them is averaged over.
http://arxiv.org/abs/hep-th/0106112
Eternal Black Holes in AdS
Juan M. Maldacena

I wonder if this has held up?

http://arxiv.org/abs/hep-th/9903237
AdS/CFT and the Information Paradox
D.A. Lowe, L. Thorlacius

http://arxiv.org/abs/0811.0263
Black Holes as Effective Geometries
Vijay Balasubramanian, Jan de Boer, Sheer El-Showk, Ilies Messamah

http://arxiv.org/abs/0909.1038
The information paradox: A pedagogical introduction
Samir D. Mathur
 
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  • #3
atyy said:
In a spacetime with a black hole, where is the horizon in the CFT?

Also, if a black hole spacetime corresponds to a thermal CFT, doesn't that mean the CFT is in a box where there is still a universe outside to provide a temperature?

You have to assume that the black hole is coupled to a heat bath such that the temperature remains constant and it's in thermal equilibrium. Then the black hole will remain at some temperature forever.


The CFT is finite and unbounded as is the horizon of the black hole. So the CFT isn't in a box since a box has bounds. Therefore the CFT doesn't need a heat bath because there is no where for the heat to flow from/to. So the whole CFT is the horizon.
 
  • #4
Finbar said:
You have to assume that the black hole is coupled to a heat bath such that the temperature remains constant and it's in thermal equilibrium. Then the black hole will remain at some temperature forever.


The CFT is finite and unbounded as is the horizon of the black hole. So the CFT isn't in a box since a box has bounds. Therefore the CFT doesn't need a heat bath because there is no where for the heat to flow from/to. So the whole CFT is the horizon.

So if the CFT is the whole universe, then the universe will be in a mixed state - but how can that be - quantum mechanically, shouldn't there be only pure states when it comes to the whole universe?
 
  • #5
atyy said:
So if the CFT is the whole universe, then the universe will be in a mixed state - but how can that be - quantum mechanically, shouldn't there be only pure states when it comes to the whole universe?

In the case of the eternal black hole discussed by Maldecena in your first link, there are actually two copies of the CFT. The black hole geometry is an approximate description of an entangled state of the two CFTs. This entangled state has the property that it looks exactly thermal to each CFT individually. Additionally, the CFTs are unable to communicate due to the black hole horizons.
 

1. What is the AdS/CFT correspondence?

The AdS/CFT correspondence is a conjectured duality between two seemingly different theories: Anti-de Sitter space (AdS), which is a spacetime with negative curvature, and conformal field theory (CFT), which is a quantum field theory without gravity. This duality suggests that these two theories are actually equivalent, meaning that they describe the same physics in different mathematical languages.

2. What is the significance of the horizon in AdS/CFT?

In the context of AdS/CFT, the horizon refers to the event horizon of a black hole in AdS space. This horizon is important because it allows us to study the properties of black holes in a different way, using the dual CFT. This provides a new perspective on black hole physics and has led to new insights and discoveries.

3. How does the CFT in black hole spacetime work?

The CFT in black hole spacetime is a quantum field theory living on the boundary of AdS space, which is dual to the black hole in the bulk. The CFT describes the behavior of the black hole in terms of the microscopic degrees of freedom on its horizon. This allows us to study the thermodynamics and information loss paradox of black holes in a different way.

4. What are some applications of the AdS/CFT correspondence?

The AdS/CFT correspondence has been applied to various fields, including quantum gravity, string theory, and condensed matter physics. It has provided a new way to study and understand black holes, and has also led to new insights into the nature of quantum gravity. In condensed matter physics, it has been used to model strongly coupled systems and has provided a new framework for understanding phase transitions.

5. Is the AdS/CFT correspondence proven?

The AdS/CFT correspondence is a conjecture, meaning that it has not been proven mathematically. However, there is a large body of evidence supporting its validity, including numerous successful calculations and agreements between the dual theories. It is also consistent with other known theories, such as string theory. However, further research and investigation is still ongoing to fully understand and prove the correspondence.

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