Before 1995 the main stream belief of the physics community was that there were exactly five consistent superstring theories (here on referred to as string theories), which were given the names Type I string theory, Type IIA string theory, Type IIB string theory, heterotic SO(32) (the HO string) theory, and heterotic E8×E8 (the HE string) theory. The five theories all share essential features that relate them to the name of string theory. Each theory is fundamentally comprised of vibrating, one dimensional strings at approximately the length of the Planck length. Calculations have also shown that each theory requires more than the normal four spacetime dimensions (although all extra dimensions are in fact spatial.) However, when the theories are analyzed in detail, significant differences appear.
The Type I string theory has vibrating strings like the rest of the string theories. These strings vibrate in closed loops, so that the strings have no ends. However, one difference that separates the Type I string theory from the other four string theories is that the Type I string theory also contains open strings, vibrating strings with two loose ends. This was a feature that the other string theories did not contain (The Type IIA and Type IIB string theories also contain open strings, however these strings are bound to D-branes). Furthermore, calculations show that the list of string vibrational patterns and the way each pattern interacts and influences others vary from one theory to another. These and other differences hindered the development of the string theory as being the theory that united quantum mechanics and general relativity successfully. The general aim of the physics community was to eliminate four of the theories, having only one theory to explain string theory. However, this approach proved incorrect, and instead the correct approach became that of unifying the five string theories by examining certain identifications and dualities.
As the names suggest, some of these string theories were thought to be related to each other. In the early 1990s, string theorists discovered that some relations were so strong that they could be thought of as an identification. The Type IIA string theory and the Type IIB string theory were known to be connected by T-duality; this essentially meant that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R, where distances are measured in units of the Planck length.
This was a profound result. First, this was an intrinsically quantum mechanical result the identification did not hold in the realm of classical physics. Second, because it is possible to build up any space by gluing circles together in various ways, it would seem that any space described by the IIA string theory can also be seen as a different space described by the IIB theory. This implies that the IIA string theory can identify with the IIB string theory: any object which can be described with the IIA theory has an equivalent, although seemingly different, description in terms of the IIB theory. This suggests that the IIA string theory and the IIB string theory are really aspects of the same underlying theory.
There are other dualities between the other string theories. The heterotic SO(32) and the heterotic E8×E8 theories are also related by T-duality; the heterotic SO(32) description of a circle of radius R is exactly the same as the heterotic E8×E8 description of a circle of radius 1/R. There are then really only three superstring theories, which might be called (for discussion) the Type I theory, the Type II theory, and the heterotic theory.
There are still more dualities, however. The Type I string theory is related to the heterotic SO(32) theory by S-duality; this means that the Type I description of weakly interactingstrongly interacting particles can also be seen as the heterotic SO(32) description of very particles. This identification is somewhat more subtle, in that it identifies only extreme limits of the respective theories. String theorists have found strong evidence that the two theories are really the same, even away from the extremely strong and extremely weak limits, but they do not yet have a proof strong enough to satisfy mathematicians. However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.
At this point, there are only two string theories: the heterotic string theory (which is also the type I string theory) and the type II theory. There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.
This last step, however, is the most difficult and most mysterious. It is best explained first in a certain limit. In order to describe our world, strings must be extremely tiny objects. So when one studies string theory at low energies, it becomes difficult to see that strings are extended objects — they become effectively zero-dimensional (pointlike). Consequently, the quantum theory describing the low energy limit is a theory that describes the dynamics of these points moving in spacetime, rather than strings. Such theories are called quantum field theories. However, since string theory also describes gravitational interactions, one expects the low-energy theory to describe particles moving in gravitational backgrounds. Finally, since superstring string theories are supersymmetric, one expects to see supersymmetry appearing in the low-energy approximation. These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory.
The possible supergravity theories were classified by Werner Nahm in the 1970s. In 10 dimensions, there are only two supergravity theories, which are denoted Type IIA and Type IIB. This is not a coincidence; the Type IIA string theory has the Type IIA supergravity theory as its low-energy limit and the Type IIB string theory gives rise to Type IIB supergravity. The heterotic SO(32) and heterotic E8×E8 string theories also reduce to Type IIA and Type IIB supergravity in the low-energy limit. This suggests that there may indeed be a relation between the heterotic/Type I theories and the Type II theories.
In 1994, Edward Witten outlined the following relationship: The Type IIA supergravity (corresponding to the heterotic SO(32) and Type IIA string theories) can be obtained by dimensional reduction from the single unique eleven-dimensional supergravity theory. This means that if one studied supergravity on an eleven-dimensional spacetime that looks like the product of a ten-dimensional spacetime with another very small one-dimensional manifold, one gets the Type IIA supergravity theory. (And the Type IIB supergravity theory can be obtained by using T-duality.) However, eleven-dimensional supergravity is not consistent on its own — it does not make sense at extremely high energy, and likely requires some form of completion. It seems plausible, then, that there is some quantum theory — which Witten dubbed M-theory — in eleven-dimensions which gives rise at low energies to eleven-dimensional supergravity, and is related to ten-dimensional string theory by dimensional reduction. Dimensional reduction to a circle yields the Type IIA string theory, and dimensional reduction to a line segment yields the heterotic SO(32) string theory.
Taking seriously the notion that all of the different string theories should be different limits and/or different presentations of the same underlying theory, the concept of string theory must be expanded. But little is known about this underlying theory. The bonus is that all of the different string theories may now be thought of as different limits of a single underlying theory.
|Wikipedia|
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