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I was reading a paper by Veronika Hubeny The AdS/CFT correspondence 1. Maldacena chose a D3-brane system to derive his conjecture. So I was wondering, why "D3-brane"? In other words, I need to know the importance of D3-brane system, so that is used in the AdS/CFT correspondence. It would be nice if a reference is recommended if the answer isn't so straightforward. Thanks in advance.

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    $\begingroup$ Have you tried reading the original paper by Maldacena (arxiv.org/pdf/hep-th/9711200.pdf)?, or the review by Maldacena, Ooguri, et al (arxiv.org/abs/hep-th/9905111), or the review by D'hoker and Freedman (arxiv.org/abs/hep-th/0201253)?. D3 branes are the key elements in the derivation of the AdS/CFT conjecture. But you could be more precise, what is your background in String Theory, Supergravity, QFT, etc? $\endgroup$ – Jasimud Sep 5 '16 at 2:09
  • $\begingroup$ Thanks, I will check them. I'm new to all this. I had a QFT course but this is my first paper concerning AdS/CFT, and I have just read some parts of Zweibach's book (A first course in String Theory). $\endgroup$ – Milou Sep 5 '16 at 2:16
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$3$-branes are special in the following sense: only for $p=3$, the black p-brane solution admits a constant dilaton, while it is running for $p\not=3$. In particular, the dilaton $\phi$ diverges at the horizon of extremal $p$-brane solutions for $p\not=3$, which means that the string coupling $g_s=e^\phi$ cannot be kept small. In the Maldacena decoupling argument, two limits are taken:

  1. A near-horizon limit in the $p$-brane background
  2. A supergravity limit in which string loop corrections are supressed, i.e. $g_s\ll 1$

For $p\not=3$, the second limit cannot be taken near the horizon since the string coupling diverges. Only for $p=3$ the constant dilaton can also be taken to be small near the horizon.

In summary, only 3-brane solutions admit a simultaneous near-horizon and supergravity limit!

For all the mathematical details, you can refer to pages 16 - 19 in the MAGOO review.

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