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https://ncatlab.org/nlab/show/M-theory has statement “In this analogy, the various perturbative string theories (HET, I, IIA, IIB and their KK-compactifications) correspond to arithmetic geometries over base prime field Fp for p≥2, and the would-be M-theory corresponds to a theory of a “field with one element” that unifies all this, by describing it at a deeper level”. Is there reference for this stament? Where this analogy is elaborated. Maybe there is no reference, it may be just folklore or feeling. Then just fine, I will accept it. But if there is reference, then it would be nice to see it. Thanks.
Just to clarify, this is not a “statement” but an analogy (explicitly marked as such) that I offer as an attempt to explain to mathematicians, and by comparison to a familar situation, what it means to expect a theory to exist, as yet unknown but with limiting cases that are known.
As it goes with analogies, if it helps you are welcome, while if it does not help you are free to ignore it. But as far as analogies, go, this one is rather apt, it seems to me.
(I should clarify that we are talking about this paragraph at M-theory, which I originally wrote for the page Hypothesis H).
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