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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 ...

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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.

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Analyzing the spectrum of the strings, one finds that it contains $N^2$ massless vector states, which is precisely the number of gauge fields corresponding to a $U(N)$ group. Note that this is only true for massless oriented open strings; the unoriented case yields $SO(N)$ or $Sp(N)$. As is described in the same chapter of the book, open string states can ...

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The "math works it out" indeed. I try to write it as accessible as I can. A 0-domensional Euclidean space is just a point. The 1-dimensional is a line. The 2-dimensional is a plane. The 3-dimensional is the space as we know it. This can be continued to 4-5-6 whatever dimensions. On a plane you can draw lines and point, but not planes. In space you can ...

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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 ...

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When you try writing a quantu, theory of strings, you get supergravity in the classical limit. Branes are just solitonic solutions to those supergravity theories. You can classify string/brane theories based on the type of SUGRA theory you get in the classical limit. That gives you four kinds in (9+1)dim and M-theory in (10+1)dim, all related by various ...

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