Silly question about n.of dimensions in m-theory

[matteo210]

hi everyone,

i am no physicist so i only have a slight understanding of these matters.
I just finished reading Greene's "elegant universe" and i understood that in "classical" string theories there are 6 compactified dimensions along with our familiar 3 extended spatial dimensions + time.

From what Greene writes, M-theory (following supersimmetry/supergravity theories) adds a further compactified dimension which is different from the other ones because it is "embedded" in the strings themselves. I mean, if i understood correctly (which i doubt), the six compactified dimensions are "external" to the strings and they add further degrees of freedom to the strings'movements and vibrations. The seventh dimension is instead "embedded" in the strings, so that a string can become a 2-brane.

If the above is true, why then are we only adding one further dimension? given the fact that branes can have n dimensions, why the m-theory only adds one further compactified dimension and not n further dimensions?
Hope i made myself sufficiently clear, thanks for an answer,
matteo

 

[Demystifier]

A good question. Indeed, M-theory (viewed as an unknown unification theory that contains strings as a special case) could, in principle, have more than 11 dimensions. However, we know that it has AT LEAST 11 dimensions. The belief that M-theory has exactly 11 dimensions is related to the fact that the highest number of dimensions for a supersymmetric field theory (without spins higher than 2) is 11. On the other hand, there are speculations known under the name F-theory that the actual number of dimensions in the final theory could be 12.

Anyway, for MOST branes the n dimensions of the brane are NOT embedded in the strings. That's why in most cases we do not need to add further dimensions for branes.

 

[torquil]

The seventh dimension is instead "embedded" in the strings, so that a string can become a 2-brane.

I wouldn't say the dimension is "embedded in the string". I think it is just that the 1D string is extended in the extra dimension of M-theory. All the strings of string theory are really extended also in a small dimension that is neglected. If you take it into account, you see that the strings are really 2d objects.

The main reason for the one extra dimension is to unify the five different string theories, and notice that they are different limits of M-theory. Anyway, all this is quite uncertain.

Torquil

 

[arivero]

Edited:

Duff et al have an interesting approach by comparing scalar extended objects and fermions. See page 10 of http://arxiv.org/pdf/hep-th/9611203v2 contains the detailed argument. Esentially is the same argument that Demystifier, but it allows to locate all the possible extended branes. The point is that the product of the number of components of the D-dimensional spinor and the number of allowed supersymmetries in dimension D producing no spin higher than 2 is bounded, and it must match the degrees of freedom of the scalar bosons in any extended object living there.

 

[tom.stoer]

... On the other hand, there are speculations known under the name F-theory that the actual number of dimensions in the final theory could be 12

As far as I understood the 12th dimension is a technicality and not a real dimension. In addition I thought that F-theory is a local approach to describe some structures of full string- / M-theory, but w/o claiming to be the full theory. So does this additional dimension matter at all?