Apparently Sylvester James Gates Jr. has formulated a variation on string theory that does not require extra spatial dimensions (or temporal dimensions for that matter). He indicated in his lecture at the 2005 Nobel Conference at Gustavus Adolphus College that this model has not received nearly as much attention as, say M-theory, primarily due to the increased mathematical complexity and decrease in "elegance" required to make it consistent in 4 dimensions. I would like to know how such a theory could be experimentally tested, and what observational divergences it would have from conventional string theory. Any thoughts?
Do you have any link where we could read about that? Aside of that paper string theories in 4 dimensions have existed almostr from the very begining of string theory. Youu can find about them within the name "Liouville strings". Also, in the begining of the nineties, there was a large amount of work in something named "matrix models". Those models (not to confuse with some more recent matrix formulation of M-Theory in flat space times) came from doing a simplicial aproximation of 2-d quantum gravity, or quantum grvity in the world-sheet. I donĀ“t know too much about these (about the liouville model you could read the cahpter of the book "quantum field theory of point particles and strings" by Brian Hatfield if you have access to it in some library) but the general feeling seems to be that they are plagged of a lot of mostly unsumormable inconsistencies which render them useless.