• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  AdS/CFT dual of $N$ D$p$-branes at finite temperature

+ 5 like - 0 dislike

The gravity dual of $N$ D$p$-branes at zero temperature is

$$ ds^2= H^{-1/2}(r)(-dt^2+dx_p^2) + H^{1/2}(r)(dr^2 + r^2d\Omega_{8-p}^2) $$


$$ H(r) = 1 + \left(\frac{R}{r}\right)^{7-p} $$

what is (tell me if I'm wrong) an extremal black $p$-brane.

When we consider that the boundary system is at temperature $T$, the dual metric then is

$$ ds^2= H^{-1/2}(-h(r)dt^2+dx_p^2) + H^{1/2}\left(\frac{dr^2}{h(r)} + r^2d\Omega_{8-p}^2\right) \qquad(*)$$


$$ h(r) = 1 + \left(\frac{r_0}{r}\right)^{7-p} $$

(for example, this is written here, in section 7.5, for $p=3$), but I don't know to what system corresponds this metric, except for $p=3$, which is an AdS black hole (for $r$ near the throat).

So the question is, what system has the metric $(*)$?

This post imported from StackExchange Physics at 2014-10-01 20:26 (UTC), posted by SE-user David Pravos
asked Sep 30, 2014 in Theoretical Physics by David Pravos (35 points) [ no revision ]
retagged Oct 1, 2014

1 Answer

+ 3 like - 0 dislike

AdS black holes exist in various dimensions, $p=3$ is not the only choice. The parameter can take on values above or below $3$. One famous example is the three-dimensional BTZ black hole, and higher dimensional ones are also frequently used in the correspondence.

Furthermore, I think there is a misunderstanding on the concept of a "gravity dual". The metric you wrote down is not the the gravity dual of a $\mathrm{D}p$-brane at zero temperature, it is a solution of classical gravity that corresponds to the geometry of such a brane at low energies. In this sense, it is the D-brane in a particular limit. The word "gravity dual" refers to precisely this geometry, and it is the dual of a quantum field theory living on its boundary. The AdS/CFT correspondence is about formulating higher-dimensional gravity duals (D-Branes and their low energy limits) of quantum field theories in lower dimensions.

This post imported from StackExchange Physics at 2014-10-01 20:26 (UTC), posted by SE-user Frederic Brünner
answered Oct 1, 2014 by Frederic Brünner (1,130 points) [ no revision ]
But for $p\neq 3$ the first metric is not AdS. If I understood correctly your answer, the metric (*) corresponds to a black hole in the spacetime of the first metric?

This post imported from StackExchange Physics at 2014-10-01 20:26 (UTC), posted by SE-user David Pravos
Your statement is not true, AdS is not restricted to $p=3$.

This post imported from StackExchange Physics at 2014-10-01 20:26 (UTC), posted by SE-user Frederic Brünner

You would have to proceed into finding the holographic dictionary in order to get some answers, provided it exists. Your dual theory created by the specific D-brane system which exhibits this geometry (*) would probably be some kind of SYM at finite temperature. At least this is the general idea when someone wants to get intuition on the dual theory.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights