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I was reading an article about the existence of exotic spheres in 7 dimensions, my initial instinct was that that was pure mathematics and most likely inapplicable to any natural sciences. Then I remembered string theory used 10 spatial dimensions, so, are there structures in string theory that are equivalent to exotic spheres? Does it imply that the metric of space-time becomes non-smoothable, despite being continuous?

Will Graham
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    More on exotic differential structures: http://physics.stackexchange.com/q/43683/2451 , https://physics.stackexchange.com/q/264033/2451 – Qmechanic Apr 30 '17 at 05:01

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In a paper I do not understand Witten suggests that exotic spheres can represent gravitational instantons.

In the other direction, Gregory Moore writes "There have been ample opportunities for exotic differentiable structures on $S^7$ and $S^{11}$ to play an important role in 11-dimensional supergravity, but again nothing compelling has emerged." He does add "Yet."

And back in the first direction (but quite speculatively) Moore, in the same paper, suggests that there might be some physics lurking behind the fact that the number of exotic $11$-spheres ($992$) is exactly four times the dimension of $E_8$.

WillO
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