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As far as I know, mirror symmetry has its origins in the Kaluza-Klein idea where the extra dimensions of spacetime are "curled up" or "compactified" into a Calabi-Yau manifold, which is why we see only 4 dimensions of spacetime (I think the "size" of this Calabi-Yau manifold is supposed to be very small).

Now a Calabi-Yau manifold is very interesting, since it is a Kahler manifold, and has a Riemannian, a symplectic, and a complex structure, and mirror symmetry explores how these structures behave under the dualities of string theory.

AdS/CFT, on the other hand, is kind of a different idea, where the reason why we only see 4 dimensions of spacetime is because we live on the "boundary" of some larger space, which involves the anti-DeSitter geometry. Are the concepts related to mirror symmetry still relevant in AdS/CFT?

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  • $\begingroup$ What do you mean by "still relevant"? $\endgroup$ – Antoine May 16 '18 at 18:43

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