# $D$-brane and 5th dimensions

While I was looking up the 5th dimension of the Randall-Sandram model, I have wondered whether Kaluza Klein theory can be applied to the $D$-brane or $p$-brane.

Can the $D$-brane and $p$-brane wrapped as compactification of the dimensions?

If so, what is the main difference between $D$- and $p$-brane?

• Have you tried the obvious Google searches? If so, can you be more specific about what you're asking? – John Rennie May 6 '14 at 10:36
• Main question was whether the D-brane and P-brane can be wrapped up or not . It seems the answer can be accessed through the Google Search if you say so. – user44629 May 6 '14 at 10:51
• The "p" in p-brane stands in for the number of spatial dimensions that a brane covers. The "D" in D-brane stands for something quite different: It states that this brane provides "Dirichlet" boundary conditions for the strings roaming around in space. – Siva Oct 13 '14 at 20:26

The answer is yes, branes (both $D$ and $p$) can be wrapped around compactified dimensions. There is little difference between the two types of branes with regard to compactification.
String theories are consistent in 26 (bosonic string theory), 10 (superstring theories) and 11 (M-theory) dimensions. To get our world (4D) one needs to compactify the extra-dimensions. In general $D$ branes are extended $p+1$ dimensional objects with $p$ spatial and one time dimension. Obviously, if $p>d$ (here $d$ is the dimension of theory you want to get after compactification) then some of D brane dimensions are compact. For example, compactifying superstring theory to 4D we have 6 compact dimensions and if there is a brane with $p>4$ then it has some compact coordinates. So the answer on your first question is Yes.
From the definition that I gave above, you see that if you want to specify the dimension of $D$ brane you call it $Dp$ brane. Now why $D$? Actually there are two other types of branes - $NS$ and $M$ branes, so that is why we need a letter $D$ - to distinguish different types of branes.