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?

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    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
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    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.

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

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.

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

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.

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