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Request to String Lovers: Classify theories by critical dimensions.

  1. Jan 13, 2009 #1

    MTd2

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    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. jcsd
  3. Jan 13, 2009 #2
    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.
     
  4. Jan 13, 2009 #3

    MTd2

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    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.
     
  5. Jan 13, 2009 #4
    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.
     
  6. Jan 13, 2009 #5

    MTd2

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    Yes, that's why I included calculatinal device above. Do you know any other?
     
  7. Jan 13, 2009 #6

    atyy

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    Would you count gauge/gravity dualities?
     
  8. Jan 13, 2009 #7

    MTd2

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    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?
     
  9. Jan 13, 2009 #8

    MTd2

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  10. Jan 13, 2009 #9

    MTd2

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    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.
     
  11. Jan 13, 2009 #10
    How are these dimensions?
     
  12. Jan 13, 2009 #11

    atyy

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    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.
     
  13. Jan 13, 2009 #12

    MTd2

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    I was thinking about F-Theory, something that gives any kind of strings at lower dimensions...
     
    Last edited: Jan 13, 2009
  14. Jan 13, 2009 #13
    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.
     
  15. Jan 14, 2009 #14

    atyy

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    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
     
  16. Jan 14, 2009 #15
    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.
     
  17. Jan 14, 2009 #16

    Demystifier

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    Can somebody recommend me the relevant literature to learn more about this?
     
  18. Jan 14, 2009 #17

    MTd2

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  19. Jan 14, 2009 #18

    Demystifier

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    Thanks MTd2!
     
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