# Request to String Lovers: Classify theories by critical dimensions.

1. Jan 13, 2009

### MTd2

Topological Strings = 3
Superstrings = 10
Bosonic strings 26
Tensionless strings = arbitrary

Do you know of any others that could fit in other dimensions not listed above?

2. Jan 13, 2009

### BenTheMan

Mtheory has 11 dimensions.

I don't know if you can see a tensionless string as a limit of Mtheory, but all of the superstring theories can be seen from MTheory and some dualities.

Also, bosonic string theory is only a toy model, and it was never really expected that it be realistic. We only study it as an introduction.

3. Jan 13, 2009

### MTd2

Sure, I am just looking for listing theories, it doesn't matter if they are realistic or not, or if the extre dimensions are just a calculational device or help. :). Just trying to see if there is something curious around.

Another one. F-Theory has 12 dimesions.

So, we have:

Topological Strings = 3
Superstrings = 10
M -Theory = 11
F - Theory = 12
Bosonic strings = 26
Tensionless strings = arbitrary

More? I guess I saw something today with 13 dimensions.

4. Jan 13, 2009

### BenTheMan

Well, the 11th and 12th dimensions of Ftheory are just a tool. They are not physical "space" dimensions as some have said. And either way, Ftheory is just a limit of Mtheory.

5. Jan 13, 2009

### MTd2

Yes, that's why I included calculatinal device above. Do you know any other?

6. Jan 13, 2009

### atyy

Would you count gauge/gravity dualities?

7. Jan 13, 2009

### MTd2

Hmm. I haven't thought about that... But I guess that wouldn't be very stringy, since unlike m theory where you get strings should arise from compactification, that one would be sort of classical limit coming from strings, isn't it?

8. Jan 13, 2009

### MTd2

I found this:

4-D FERMIONIC SUPERSTRINGS FROM THIRTEEN-DIMENSIONS: sigma MODEL AND SUPERCONFORMAL PROPERTIES

D'Auria, R.;Fre, P.;Gliozzi, F.;Pasquinucci, A

http://www-lib.kek.jp/cgi-bin/kiss_prepri.v8?KN=200034725&OF=4 [Broken].

Last edited by a moderator: May 3, 2017
9. Jan 13, 2009

### MTd2

http://arxiv.org/abs/hep-th/9204071

Twistor-like superstrings with D = 3, 4, 6 target-superspace and N = (1,0), (2,0), (4,0) world-sheet supersymmetry
Authors: F. Delduc, E.Ivanov, E. Sokatchev
(Submitted on 22 Apr 1992)

Abstract: We construct a manifestly $N=(4,0)$ world-sheet supersymmetric twistor-like formulation of the $D=6$ Green-Schwarz superstring, using the principle of double (target-space and world-sheet) Grassmann analyticity. The superstring action contains two Lagrange multiplier terms and a Wess-Zumino term. They are written down in the analytic subspace of the world-sheet harmonic $N=(4,0)$ superspace, the target manifold being too an analytic subspace of the harmonic $D=6\;\; N=1$ superspace. The kappa symmetry of the $D=6$ superstring is identified with a Kac-Moody extension of the world-sheet $N=(4,0)$ superconformal symmetry. It can be enlarged to include the whole world-sheet reparametrization group if one introduces the appropriate gauge Beltrami superfield into the action. To illustrate the basic features of the new $D=6$ superstring construction, we first give some details about the simpler (already known) twistor-like formulations of $D=3, N=(1,0)$ and $D=4, N=(2,0)$ superstrings.

10. Jan 13, 2009

### BenTheMan

How are these dimensions?

11. Jan 13, 2009

### atyy

Well, the dimensions in the gauge theory are different from the gravity theory. So if MTd2 wanted "calculational devices" then maybe he would consider those too.

12. Jan 13, 2009

### MTd2

I was thinking about F-Theory, something that gives any kind of strings at lower dimensions...

Last edited: Jan 13, 2009
13. Jan 13, 2009

### BenTheMan

Sorry for being dense, but in what sense is this true?

The dimensions in gauge theory still enter in terms of a metric, the same way they enter in GR. Maybe I'm missing something.

14. Jan 14, 2009

### atyy

More likely I'm being dense since it's from a bunch of stuff I'm still trying to understand. Anyway, I'm thinking of statements like "On both sides of the duality we have started in D = 10, because this is the natural dimensionality for this supersymmetry algebra. On the gauge side, however, this was just a device to give a compact description of the Lagrangian; the field theory lives in four dimensions. On the gravity side, the quantum theory is fully ten-dimensional, not just a dimensional reduction." in Horowitz and Polchinksy's http://arxiv.org/abs/gr-qc/0602037

15. Jan 14, 2009

### BenTheMan

Well, the dualities are usually a strong/weak coupling duality (in the case you're talking about) or a big/small duality.

What you find in the gauge/gravity duality is that you can describe all of the degrees of freedom in a strongly coupled gauge theory using a (weakly coupled) gravity theory. This is nice, because it's the only way we _really_ know how to deal with strongly coupled theories.

16. Jan 14, 2009