sage
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Physics Benchmarks of string theory 7.: AdS-CFT
The famous AdS-CFT also started from a very physical intuition of the
physics of blackholes. After the work of Hawking, we know that the
blackholes have entropy. Moreover, it scales like the area of the
blackhole. Entropy counts the degrees of freedom in a
system. Therefore, Hawking radiation suggests that the number of
degrees of freedom of a blackhole is proportional to the area its
horizon. On the other hand, physically, this is very
strange, because intuitively, the number of degrees of freedom in a
system should proportional to it volume.
Therefore, somehow, gravity is very strange. It seems that for a
blackhole, its number of degrees of freedom of the gravitational
system seem to be live on the surface or boundary. It seems that
the information of gravity in higher dimension is encoded on the
boundary of the spacetime.
Based on this, 't Hooft was the first to propose the so called
holographic principle, which means information about quantum gravity
lives on its lower dimensional boundary.
Many people thinks this is true. However, for a while, nobody is able
to make it more precise.
J. Maldacena succeeded in doing that. He construct a system in which
its higher dimenisonal description (AdS_5 * S^5) is exactly
equaivalent to a gauge theory living on the boundary (a N=4 super Yang
Mills that is conformal). This is the so called AdS-CFT
correspondence.
I would say it is one of the deepest insights about gravity we have
ever had.
The correspondence has a flip side as well. We can hope to study gauge
theory using gravity. Why do we want to do that? there are famous
problems in gauge theory still unknown to us. the most famous example
is confinement. Attempts to understand confinement from the gravity
side is now a major application of the AdS-CFT correspondence.
Such a correspondence also provided us with a large amount of
intuition for the particle physics in the AdS, such as in a
Randall-Sundrum scenario.
| 发表时间：2005-09-30, 16:24:18 |
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轩轩
发表文章数: 1352
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Re: Physics Benchmarks of string theory 7.: AdS-CFT
ADS/CFT需要一个5维度的ADS宇宙，还叉一个很小的5球面？？
那么显然这里没有卡丘空间？？？ string既然强调CY。
我们的宇宙被认为是5维度的ADS宇宙其中的一个膜？？
Therefore, Hawking radiation suggests that the number of
degrees of freedom of a blackhole is proportional to the area its
horizon.
这里horizon如果对于动态的黑洞，EH与AH不重合，选择哪一个？
引力是非局部的，量子力学也是非局部的。《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-09-30, 21:01:09 |
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sage
发表文章数: 1125
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Re: Physics Benchmarks of string theory 7.: AdS-CF
ADS/CFT需要一个5维度的ADS宇宙，
Yeah. as Randall-Sundrum. That's because the isometry of a AdS5 is the conformal group in D=4.
还叉一个很小的5球面？？
this is not essential. However, if you would like a N=4 Super-Yang-Mills, which is conformal, S^5 is a natural choce.
那么显然这里没有卡丘空间？？？
No. There is no Calabi-Yau
string既然强调CY。
String theory does not necessarily need C-Y.
我们的宇宙被认为是5维度的ADS宇宙其中的一个膜？？
That is one of the possible setups.
这里horizon如果对于动态的黑洞，EH与AH不重合，选择哪一个？
There is a matching in this case. you should look it up yourself.
| 发表时间：2005-10-01, 10:32:54 |
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追忆
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Re: Physics Benchmarks of string theory 7.: AdS-CFT
M-theory or Type ⅡB string lives on AdS space is conjectured to be dual to a conformal field theroy on the boundary of AdS space.
does it only that lives on the AdS_5 * S^5 space can be useful in giving more precise data about large 's Hooft coupling the limit of the four--demension N=4 super yang -mills field ,which is conformal and lives on the boundary of AdS_5 space ?
it is known that M-theory on AdS_4 * S^7 or AdS_7 * S^4 is dual to either three or six --demension conformal field , but these construction is out of super Gravity , remain elusive.
青山隐隐水迢迢，秋尽江南草木凋；
二十四桥明月夜，玉人何处教吹萧？
| 发表时间：2005-10-02, 05:27:48 |
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sage
发表文章数: 1125
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Re: Physics Benchmarks of string theory 7.: AdS-CF
>does it only that lives on the AdS_5 * S^5 space can be useful in giving more precise
>data about large 's Hooft coupling the limit of the four--demension N=4 super
>yang -mills field ,which is conformal and lives on the boundary of AdS_5 space ?
I don't understand what you are trying to ask here. could you break it into several sentences?
AdS5*S5 is the setup in the original AdS-CFT conjecture by Maldacena. there are a lot of other similar setups contructed by others later on, with slightly difference purposes and properties.
what is important is not the detailed setup. the true insight is the fact the a higher dimensional theory could have its information store on a lower dimensional boundary.
Studying some special setup is not very meaningful unless it has a very unique physics motivation.
| 发表时间：2005-10-02, 13:09:07 |
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