# Branes and strings connection

1. Apr 25, 2004

### ice

I was watching the Elegant Universe on PBS, and the show was talking about the string theory. there was one thing that i didnt really get though. It was the relation between strings and branes. I think i heard that if you were to add energy to a string, it gets bigger, and is stretched into a brane. but i'm not sure. please help me understand this. and if what i heard from the show was right, are there differences between the branes formed by open strings and closed strings? please help, am only in grade 11 and understanding something like this will make me seem extremely smart.

2. Apr 26, 2004

### Javier

First, let's clear up terminology. p-branes (where p=0,...,10) and "fundamental strings" are distinct objects in what we all "String theory". Fundamental strings are the ones appearing in the original formulation of string theory, but since the mid 90's, it was realized that there are also objects in the spacetime called (D)p-branes on which open strings can attach themselves. D stands for particular boundary conditions that the ends of the string must satisfy to attach the the p-branes.

What you are most likely referring to in your post is the fact that a 2-brane in 11 spacetime dimensions can wrap around a circular dimension (that is, assuming you make one of the 10 *spatial* dimensions compact). As you shrink this circular dimension, it becomes harder to probe it, and the universe looks 10-dimensional. The membrane that is wrapped looks like a fundamental string in this 10-dimensional universe.
From the reverse perspective, if you have a particular 10-dimensional string theory and you increase the coupling strength of the strings, you start being able to probe an 11-th dimension and the string looks like a 2-brane in the full 11-dimensional spacetime. (The reason for this is because the 10-dimensional coupling strength is related to the radius of the circular dimension; the origin of this relationship is not obvious).

Anyway, this relationship between branes and strings is a special circumstance where the branes are wrapped on compact dimensions (like a rubber band around a bottle, the point is they can't be removed from being in the circular direction) and then you take a limit of small or large radius.

More generally, the existence of branes is useful in that it provides a connection between closed and open string theories: you can have closed strings approach a brane, and attach themselves becoming open strings with endpoints on the brane. The reverse can happen as well. A brane can be seen as a "classical solution" to the theory, and its "quantum excitations" are described by string states attached to the brane.
Cheers.