# Is it possible that strings are higher dimensional branes?

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1. Jul 16, 2015

### Nav

Are strings really just one dimensional? Is it possible that strings are 3 dimensional? Or even 10 dimensional?

2. Jul 16, 2015

### andrewkirk

If they had more than one dimension, they would not be called strings.

There is something called 'brane theory' (brane is short for membrane) that has big membranes wobbling around in a many-dimensional manifold, with exciting things happening when they touch. In common language, a membrane is two-dimensional. So I imagine Branes have two dimensions, although it could be 'two or more'.

3. Jul 16, 2015

### Nav

but what if they are like a string like a string on a guitar which has 3 dimensions

4. Jul 16, 2015

### JorisL

Strings as is are really one dimensional. By definition. The same as point particles being zero dimensional (point particles $\neq$ atoms/nuclei although we often approximate those as points) by definition
In string theory there are several objects of higher dimensions. The ones you encounter quite soon in modern treatments are D-branes.
And a first idea about why they exist (that I've encountered so far) have to do with 'fixing' the endpoints of the string.

5. Jul 16, 2015

### phinds

A "string" on a guitar is not a string in that sense, BECAUSE it is 3D. It is a tube with length, breath, and height, not a string

6. Jul 16, 2015

### Nav

Is it possible that strings are higher dimensional branes but are just more compacted to seem like they are one dimensional when in reality they are more?

7. Jul 16, 2015

### cosmik debris

It's the other way around, branes are like higher dimensional strings.

8. Jul 16, 2015

### rootone

Or even 24 dimensional, that works too.
Have to remember that string theory is not as yet supported by evidence, though a lot of people like the idea.

9. Jul 16, 2015

### fzero

There are models where higher-dimensional membranes can wrap a compact surface to give a string-like object in the noncompact dimensions. When the wrapped object is a so-called D-brane, these are sometimes called D-strings to distinguish them from the fundamental string. Also, in one version of M-theory, starting from 11D spacetime, a membrane (two-dimensional object) is wrapped on a circle to form the fundamental string of the so-called IIA string theory in 10D spacetime. There is some discussion at a very basic level at http://superstringtheory.com/basics/basic7.html

10. Jul 16, 2015

### cosmik debris

I think you may be thinking of 26-D bosonic string theory, it is not the strings that are 26-D that is the space they live in.

11. Jul 17, 2015

### haushofer

You end up with branes, and as far as I know the action of such a brane is not renormalizable, and we don't know how to write a Polyakov-like action like we know for strings. I'm also not sure how you could quantize such an action.

12. Jul 21, 2015

### samalkhaiat

The Polyakov action of a p-brane (in D-dimensional spacetime) is just the (p+1)-dimensional Sigma model: $$S[X] \sim \int d^{p+1} \sigma \ \sqrt{-\gamma} \ \gamma^{ij}(\sigma) \ \partial_{i}X^{\mu}(\sigma) \ \partial_{j}X^{\nu}(\sigma) \ g_{\mu \nu}(X) ,$$ where $\sigma = (\sigma^{0} , \sigma^{1} , \cdots , \sigma^{p})$ are the world-volume coordinates and $X^{\mu}, \ \mu = 0, 1, \cdots , D-1$ are the spacetime coordinates of the brane: mapping of the (p+1)-dimensional parameter space of the p-brane into spacetime.
Notice that for $p = 0$, the above action becomes that of a point particle, i.e. 0-brane is point particle. For $p=1$, you get the Polyakov action for string, i.e. 1-brane is string, and 2-brane is a membrane, etc.
When a p-dimensional object moves in spacetime, it sweeps out a (p+1)-dimensional tube. This fact can be used to write a Polyakov-type action for any value of p.

Sam

13. Oct 30, 2015

### Darryl

I think if lower dimensional object can exist in higher dimensional space, then yes there is no reason (to me) that something can exists and have length but no height or width. Which any number of 1d objects and exist in a 2d space. So is a brane a 2d object composed of 1d strings? Our Universe is a 3d object in 4d space? Could those universes be separated by the 4th dimension?