# Type I' String theory as M-theory compactified on a line segment?

I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory).

That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length scales and coupling constant are inverted. So, since inverting the length scale of the theory before inverting the coupling constant is the same as inverting the coupling constant before the length scale, I think the S-dual of the T-dual of the Type I String theory is the same as the T-dual of the S-dual of the Type I String theory. The S-dual of the Type I string theory is the Type HO String theory. The T-dual of the Type HO string theory is the Type HE String theory.

Therefore, the S-dual of the Type I' String theory is the Type HE String theory. But the Type HE String theory is S-dual to M-theory compactified on a line segment.

So does this mean that the Type I' String theory is M-theory compactified on a line segment?

Thanks!

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M-theory on a line segment only is the Hořava-Witten M-theory, a dual description of the $E_8\times E_8$ heterotic string, because every 9+1-dimensional boundary in M-theory has to carry the $E_8$ gauge supermultiplet. The extra compactified circle is needed to break the $E_8\times E_8$ gauge group to a smaller one; and to get the right number of large spacetime dimensions, among other things.
Dear @dimension10, T-duality always requires some dimensions to be compactified on a circle or for type I', on line segment. For 10D string theories, T-duality relates two theories with a circular dimension (of inverse radii) and 8+1 large dimensions. It is nonsense to ask what is the T-dual of a 10-dimensional vacuum. At most, you may understand it as the infinite $R$ limit of some vacua; the T-dual is formally a singular $R=0$ compactification. Let me also mention that the infinite $R$ limit of type I' = type IA looks like type IIA string theory everywhere away from the orientifold planes. –  Luboš Motl May 26 '13 at 7:43