Quote:
Originally Posted by fettouhi
OK explain me the decomposition of M-theory  .
Regards
André |
André,
For your reading pleasure:
In physics, M-theory (sometimes also called U-theory) is a proposed "master theory" that unifies the five superstring theories. Drawing on the work from a number of string theorists (including Chris Hull, Paul Townsend, Ashoke Sen, Michael Duff, and John Schwarz), Edward Witten of the Institute for Advanced Study suggested its existence at a conference at USC in 1995, and used M-theory to explain a number of previously observed dualities, sparking a flurry of new research in string theory called the second superstring revolution.
In the early 1990s, it was shown that the various superstring theories were related by dualities, which allow physicists to relate the description of an object in one string theory to the description of a different object in another theory. These relationships imply that each of the string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".
M-theory is not yet complete; however it can be applied in many situations (usually by exploiting string theoretic dualities). The theory of electromagnetism was also in such a state in the mid-19th century; there were separate theories for electricity and magnetism and, although they were known to be related, the exact relationship was not clear until James Clerk Maxwell published his equations. Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language. However, some scientists (e.g. Peter Woit) have questioned the tangible successes of M-theory given its current incompleteness, and limited predictive power, even after so many years of intense research.
It was believed before 1995 that there were exactly five consistent superstring theories, which are called, respectively, the Type I string theory, the Type IIA string theory, the Type IIB string theory, the heterotic SO(32) (the HO string) theory, and the heterotic E8×E8 (the HE string) theory.
As the names suggest, some of these string theories are 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 are connected by T-duality; this means, essentially, 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 is a profound result. First, it is an intrinsically quantum mechanical result; the identification is not true classically. Second, because we can 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 means that we can actually identify the IIA string theory 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 theory and the IIB theory are really aspects of the same underlying theory.
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 interacting particles can also be seen as the heterotic SO(32) description of very strongly interacting 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.
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 particles 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.
The name M-theory is slightly ambiguous. It can be used to refer to both the particular eleven-dimensional theory which Witten first proposed, or it can be used to refer to a kind of theory which looks in various limits like the various string theories. Ashoke Sen has suggested that more general theory could go by the name U-theory, which might stand for Ur, Uber, Ultimate, Underlying, or perhaps Unified. (It might also stand for U-duality, which is both a reference to Sen's own work and a kind of particle physics pun.)
M-theory in the following descriptions refers to the more general theory, and will be specified when used in its more limited sense.
Prior to M-theory, strings were thought to be the single fundamental constituent of the universe, according to string theory. When M-theory unified the five superstring theories, another fundamental ingredient was added to the makeup of the universe - membranes. Like the tenth spacial dimension, the approximate equations in the original five superstring models proved too weak to reveal membranes. A membrane, or brane, is a multidimensional object, usually called a p-brane, with p referring to its spacial dimensional makeup. The p-branes can be any number of spacial dimensions ranging from zero to nine.
The inclusion of p-branes does not render previous work in string theory wrong on account of not taking note of these p-branes. P-branes are much more massive ("heavier") than strings, and when all higher dimensional p-branes are much more massive than strings, they can be ignored, as researchers had done unknowingly in the 1970s.
Shortly after Witten's breakthrough in 1995, Joseph Polchinski of the University of California at Santa Barbara discovered a fairly obscure feature of string theory. He found that in certain situations the endpoints of strings (strings with "loose ends") would not be able to move with complete freedom as they were attached, or stuck within certain regions of space. Polchinski then reasoned that if the endpoints of open strings are restricted to move within some p-dimensional region of space, then that region of space must be occupied by a p-brane. These type of "sticky" branes are called Dirichlet-p-branes, or D-p-branes. His calculations showed that the newly discovered D-p-branes had exactly the right properties to be the objects that exert a tight grip on the open string endpoints, thus holding down these strings within the p-dimensional region of space they fill.
Hope that explains a bit
Cheers, Sam
