I've heard the colloquial phrase "type 3 diabetes" appear a lot in talk about Alzheimers, so I'd be shocked if there isn't a lot of research going into that. I just read a book about how metabolism is related to a lot of mental disorders (depression, schizophrenia, etc.) so I think it's something that's definitely being looked at (the book is called Brain Energy, I think).
I've read it, it's quite good and full of citations. I've seen a number of studies since it came out that support it as well.
If you like that, also check out "This is Your Brain on Food" which overlaps with much of the content there, but with a bit more of a focus on the gut brain connection.
