Proof of F-Theory being equivalent to a Toroidal Compactification of M-Theory

Attribution: This question is taken from this Physics Stack Exchange question by "Trung Phan" with it's answer given by "Lubos Motl".

Question

Prove that $F=MA_{\left(T^{2}\to 0\right)}$ where "F" and "M" are F-Theory and M-Theory.

How does one solve this? It doesn't make much sense to me. F-Theory is obviously a 12-dimensional theory, whereas M-Theory is 11-dimensional, and when compactified on a torus, 9-dimensional. So, how can a 12-dimensional theory be equal to a 9-dimensional theory? This doesn't make sense to me.

Answers

Answer 1

The keyword here is T-Duality. When M-Theory is compactified on a torus, that's like compactifying it on 2 circles. When you compactify M-Theory once on a circle, you get Type IIA String Theory. If you compactify it, again on a circle, by w:c:psiepsilon:T-Duality, this is Type IIB String Theory.

By the definition of F-Theory, the conclusion follows trivially.