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Edward Witten, proposed in 1995, that the 5 versions of superstring theory, in 10 dimensions, were different ways of looking at one theory in 11 dimensions: M-theory.
Edward Witten is widely regarded as the most brilliant living physicist. Michio Kaku regarded him as the "Picasso of the physics community."
Witten works at the Institute for Advanced Study at Princeton. This is where Einstein lived the last years of his career.
M-theory came about in 1995 and is 11 dimensional. M-theory is a conjectured theory that would unify the known versions of superstring theory. M-theory is a proposed unification of superstring theory with 11-dimensional supergravity. Witten, and others, proposed that the 5 superstring theories are actually different ways of looking at one theory. In fact, the fact that there were 5 different versions of string theory was an embarrassment for physicists, since, we live in one universe, not five. This unification required one more dimension of space, bringing the grand total to: 11. This proposal sparked a period of research known as the "second superstring revolution." However, the formulation of M-theory is still incomplete.
M-theory was proposed by Edward Witten in 1995, at the University of Southern California, based on theoretical observations that the different versions of superstring theory were actually related by mathematical dualities: S-duality and T-duality. There was also a proposed relationship between superstring theory and a field theory known as 11-dimensional supergravity.
There is no final or definitive reason as to what the "M" stands for, however, it was stated by Witten, that it could stand for "magic, mystery of matrix". He even stated "murky", as the theory is not yet well along (he later regretted suggesting that one).
A diagram of string theory dualities.
Yellow = S-duality
Blue = T-duality
A duality is a situation where two or more theories, that appear to be different, are actually shown to give rise to the same physical consequences.
S-duality can apply to either quantum field theories (as in the case of Montonen-Olive duality, which compares N=4 supersymmetric Yang-Mills theory with the coupling constant g with the same theory with the coupling constant 1/g.) or to string theories. It is an equivalence of two physical theories. It relates a theory where calculations are difficult to a theory where calculations are easier.
Anton Capustin and Edward Witten showed that Montonen-Olive duality is closely related to the geometric Langlands program.
There is also Seiberg duality, which relates two versions of N=1 supersymmetric Yang-Mills theory. Nathan Seiberg conjectured this duality in 1994. It relates two supersymmetric QCDs. The two theories are not identical but agree at low energies.
There are many examples of S-duality in string theory. The existence of these string dualities reveals that these versions of superstring theory are actually physically equivalent.
How the five versions of superstring theory are related to M-theory and 11-dimensional supergravity.
M-theory contains ingredients besides strings. There are 2-dimensional objects known as membranes. There are objects with 3 dimensions, such as 3-branes, so on and so forth. This can be generalized to p number of dimensions, any number 10 or less, as that is the number of spatial dimensions in M-theory, as there is 1 of time and 11 total. At any rate, those objects are known as p-branes.
M-theory, however, has 7 compact dimensions, not 6. Thus the compact geometry is not a 6-dimensional Calabi-yau, however, in "this case one considers 7-dimensional manifolds of G2 holonomy. (Six-dimensional Calabi-Yau's have SU(3) holonomy.) The math is very challenging. Also, there are lots of issues if one wants to get realistic physics this way." This quote is from one of my email conversations with John H. Schwarz.
What is a coupling constant?
In quantum field theory and string theory, a coupling constant is a number that controls the strength of the interactions in the theory. For example, the strength of gravity is described by Newton's constant. Newton's constant appears in Newton's law of gravity and in Albert Einstein's general theory of relativity.
Duality is a situation in physics where two theories that are seemingly different are actually related in intricate and non-trivial ways. If two theories are related by a duality, that means that one can be transformed in such a way that it ends up looking like the other theory. The tow theories are said to be dual to one another under the transformation.
The two theories are mathematically different descriptions of the same phenomenon.
Ashoke Sen
S-duality
The first to propose S-duality in string theory was Ashoke Sen, in 1994,
It was shown that Type IIB superstring theory, with the coupling constant g is equivalent to the same theory with the coupling constant 1/g.
Similarly, Type I superstring theory with the coupling constant g is related to the heterotic SO(32) superstring with the coupling constant 1/g.
The existence of these dualities shows that the five superstring theories were not actually distinct theories.
T-duality
Besides S-duality, there is another duality that was instrumental in the second superstring revolution: T-duality. (Target-space duality or toroidal duality or even topological duality.)
T-duality, like S-duality, may be an equivalence between either quantum field theories or string theories.
Bala Sathiapalan was the first to note this idea, of T-duality, in an obscure paper in 1987.
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