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1. • CommentRowNumber1.
   • CommentAuthorblumpylumpy
   • CommentTimeJan 20th 2015
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   Author: blumpylumpy
   Format: TextHi, This is my first time attempting to access this site so apologies if this is posted in the wrong spot. I wanted to ask about a statement made in the String Theory FAQ, which, while it may be true, there is no citation and for the life of me I cannot find any corroboration. The statement is: "Except for one single constant: the “string tension”. From the perspective of “M-theory” even that disappears." As I understand it, the claim is that string theory has a single tune-able parameter, while M-theory does not. If this is true, could it be elaborated on somewhere (or do you just have a citation)? Thanks!

   Hi,
   
   This is my first time attempting to access this site so apologies if this is posted in the wrong spot. I wanted to ask about a statement made in the String Theory FAQ, which, while it may be true, there is no citation and for the life of me I cannot find any corroboration. The statement is:
   
   "Except for one single constant: the “string tension”. From the perspective of “M-theory” even that disappears."
   
   As I understand it, the claim is that string theory has a single tune-able parameter, while M-theory does not. If this is true, could it be elaborated on somewhere (or do you just have a citation)?
   
   Thanks!
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 20th 2015
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   Author: Urs
   Format: MarkdownItexThanks, good question. It should probably better say "string coupling" instead of "string tension" at that point. All these are closely related: * [[string tension]] $T = 1/(2\pi \alpha')$ * string scale $l_s = \sqrt{\alpha'}$ * string [[coupling constant]] $g_s = e^\lambda$ = radius of [[M-theory]] compactification circle * [[coupling constant]] of [[gravity]]: $\kappa \propto g_s (\alpha')^6 = g_s l_s^{12}$ * [[Newton's constant]] (before compactification) $G_N = \kappa^2/8\pi$ * [[Planck length]] $l_P = (8 \pi G_N)^{1/24} = \kappa^{1/12} \propto l_s g_s^{1/12}$ * [[Planck mass]] $M_p = l_p^{-1}$ See for instance these lecture notes here [arXiv:0908.0333](http://arxiv.org/abs/0908.0333). That the string coupling, which is a free parameter in string theory (though one may argue it is the dilaton background value) becomes the radius of the compactifying circle fiber from the point of view of M-theory was the big insight of [Witten 95](http://ncatlab.org/nlab/show/M-theory#Witten95). Thanks for your question. I have edited the FAQ at that point a little in order to clarify.

   Thanks, good question. It should probably better say “string coupling” instead of “string tension” at that point. All these are closely related:

   • string tension $T = 1/(2\pi \alpha')$

   • string scale $l_s = \sqrt{\alpha'}$

   • string coupling constant $g_s = e^\lambda$ = radius of M-theory compactification circle

   • coupling constant of gravity: $\kappa \propto g_s (\alpha')^6 = g_s l_s^{12}$

   • Newton’s constant (before compactification) $G_N = \kappa^2/8\pi$

   • Planck length $l_P = (8 \pi G_N)^{1/24} = \kappa^{1/12} \propto l_s g_s^{1/12}$

   • Planck mass $M_p = l_p^{-1}$

   See for instance these lecture notes here arXiv:0908.0333.

   That the string coupling, which is a free parameter in string theory (though one may argue it is the dilaton background value) becomes the radius of the compactifying circle fiber from the point of view of M-theory was the big insight of Witten 95.

   Thanks for your question. I have edited the FAQ at that point a little in order to clarify.