Which is the actual size of a generic brane?

[Sauron]

If you see the usual pictures of D-Branes or you go with the idea of the brane univereses you would get the impresion that branes are infinite planes. But, are there more viewpoints?.

I guess that tehere should be, but I am not sure (that´s why I open the thread aftheall). The most generic brane is a p-brane, whcih is nothing else that the natural generalization to most dimensions of the idea of an string. If the strings are supossed to be Planck sized a p-brane should also be so, unnles there is some strong motivation to think otherwise.

The most strightforward way to realize the p-brane idea, I belive, are the (two and five dimensional) M-branes. You need them as sources of some fields that appear in the low energy limit of M-theory (11 dimensional supergravity). From this viewpoint I see no dfinitive clue of which size they should have (probably it would depend on the supoort of the fields they are source for). But on the other hand we have dualities. Under some this dualities the M2-Brane would become an string, That would imply, I guess, that they must hae a topology S^1xI (I beeing the unit interval). That would imply that they would have Planckanian size.

Well, there are more brane fauna, and every brane has it´s own indiosincracy, so I want to consider all of them in a single post. they could be adrresed in subsequent ones...

 

[javierR]

p-branes appeared in supergravity first, as "electric" and "magnetic" field configurations (the former coupling to singular fieldstrengths, the latter being exact solutions and therefore associated with well-behaved field configurations). Then D-branes appeared as generalizations to the stringy case (with the p-branes presumed to be the long-wavelength limits of these). The solutions are taken to be infinite in directions along the branes for stability. 0-branes are "particles" that have a finite size, though for small string coupling, they are smaller than strings.
Just as a string has a tension (inversely related to its length), so do branes. 11D sugra compactified on a circle appears to give the 10D perturbative IIA string theory as the size of the circle shrinks. The 2-brane of the 11D theory is supposed to give the fundamental string of this theory as you mentioned. The tensions are required to match for the two objects. But the tension of the string is inversely proportional to the string coupling, so as you increase the coupling with the size of the circle, the tension shrinks and the size of the string enlarges, along with its new dimension, until we end with the 2-brane in the decompactified 11 dimensional theory.