How Do Strings Transform into Branes in String Theory?

[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.

 

[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.

 

[R0man]

Firstly, it's great to see that you're interested in learning about string theory at such a young age! The connection between branes and strings is a fundamental concept in string theory and can be a bit confusing at first. But don't worry, I'll try my best to explain it in a simple way.

In string theory, particles are not considered to be point-like objects, but rather tiny one-dimensional strings. These strings vibrate at different frequencies, giving rise to different particles. Now, a brane (short for membrane) is a higher-dimensional object that can be thought of as a surface in which strings can end or interact.

So, in essence, branes are like "walls" where strings can attach themselves to or interact with. When a string vibrates at a high enough frequency, it can create enough energy to stretch and form a brane. This is where the idea of a string getting bigger and forming a brane comes from.

Now, there are two types of strings - open strings and closed strings. Open strings have two endpoints, while closed strings are like loops with no endpoints. When a closed string vibrates with enough energy, it can form a brane that is closed and connected, similar to the string itself. On the other hand, when an open string vibrates with enough energy, it can form a brane that is open and has two endpoints, similar to the string itself.

In terms of differences between branes formed by open and closed strings, there are some subtle distinctions. For example, open strings can only end on certain types of branes, while closed strings can end on any type of brane. Additionally, the vibrations of open strings are restricted to their endpoints, while closed strings can vibrate along their entire length.

I hope this helps to clarify the concept of branes and strings for you. Keep exploring and learning, and who knows, you may become a future physicist studying string theory!