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.
This post imported from StackExchange Physics at 2014-10-14 10:44 (UTC), posted by SE-user g3n1uss