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

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

with

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

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

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

with

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

(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