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In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds the dimensionality of five superstring theories in 10 dimensions, it is believed that the 11-dimensional theory unifies all string theories (and supersedes them). Though a full description of the theory is not yet known, the low-entropy dynamics are known to be supergravity interacting with 2- and 5-dimensional membranes.
This idea is the unique supersymmetric theory in eleven dimensions, with its low-entropy matter content and interactions fully determined, and can be obtained as the strong coupling limit of type IIA string theory because a new dimension of space emerges as the coupling constant increases.
Drawing on the work of a number of string theorists (including Ashoke Sen, Chris Hull, Paul Townsend, 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 super string theory to the description of a different object in another super string theory. These relationships imply that each of the super string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".
Originally the letter M in M-theory was taken from membrane, a construct designed to generalize the strings of string theory. However, as Witten was more skeptical about membranes than his colleagues, he opted for "M-theory" rather than "Membrane theory". Witten has since stated that the interpretation of the M can be a matter of taste for the user of the word "M-theory".[1]
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, in his 1864 paper A Dynamical Theory of the Electromagnetic Field. Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language. However, some scientists have questioned the tangible successes of M-theory given its current incompleteness, and limited predictive power, even after so many years of intense research.
In late 2007, Bagger, Lambert and Gustavsson set off renewed interest in M-theory with the discovery of a candidate Lagrangian description of coincident M2-branes, based on a non-associative generalization of Lie Algebra, Nambu 3-algebra or Filippov 3-algebra. Practitioners hope the Bagger-Lambert-Gustavsson action (BLG action) will provide the long-sought microscopic description of M-theory.
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Prior to 1995 there were five (known) consistent fatstring theories (henceforth 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 both in closed loops, so that the strings have no ends, and as open strings with two loose ends. The open loose strings are what separates the Type I string theory from the other four string theories. 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 that is to say, they are tight).
The calculations of the String Vibrational Patterns 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. Attempts by the physics community to eliminate four of the theories, leaving only one string theory, have not been successful.
M-theory attempts to unify the five string theories by examining certain identifications and dualities. Thus each of the five string theories become special cases of M-theory.
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[2][3] 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. This implies that there are 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 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.
Given the above commonalities there appear to be 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 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 similar denomination 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.
M-theory would implement the notion that all of the different string theories are different special cases.
There are two issues to be dealt with here:
Cynics have noted that the M might be an upside down "W", standing for Witten. Others have suggested that for now, the "M" in M-theory should stand for Missing or Murky[6]. The various speculations as to what "M" in "M-theory" stands for are explored in the PBS documentary based on Brian Greene's book The Elegant Universe.
M-theory in the following descriptions refers to the more general theory, and will be specified when used in its more limited sense.
In the standard string theories, strings are assumed to be the single fundamental constituent of the universe. M-theory adds another fundamental constituent - membranes. Like the tenth spatial 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 the number of dimensions in which it exists. The value of 'P' can range from zero to nine, thus giving branes dimensions from zero (0-brane ≡ point particle) to nine - five more than the world we are accustomed to inhabiting (3 spatial and 1 time). 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, 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.
Not all strings are confined to p-branes. Strings with closed loops, like the graviton, are completely free to move from membrane to membrane. Of the four force carrier particles, the graviton is unique in this way. Researchers speculate that this is the reason why investigation through the weak force, the strong force, and the electromagnetic force have not hinted at the possibility of extra dimensions. These force carrier particles are strings with endpoints that confine them to their p-branes. Further testing is needed in order to show that extra spatial dimensions indeed exist through experimentation with gravity.
One of the reasons M-theory is so difficult to formulate is that the numbers of different types of membranes in the various dimensions increases exponentially. For example once you get to 3 dimensional surfaces you have to deal with solid objects with knot shaped holes, and then you need the whole of knot theory just to classify them. Since M-theory is thought to operate in 11 dimensions this problem then becomes very difficult. But just like string theory, in order for the theory to satisfy causality, the theory must be local, and so the topology changing must occur at a single point. The basic orientable 2-brane interactions are easy to show. Orientable 2-branes are tori with multiple holes cut out of them.
The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Super gravity. Though this formulation provided a key link to the low-energy limits of string theories, it was recognized that a full high-energy formulation (or "UV-completion") of M-theory was needed.
For an analogy, the Super gravity description is like treating water as a continuous, incompressible fluid. This is effective for describing long-distance effects such as waves and currents, but inadequate to understand short-distance/high-energy phenomena such as evaporation, for which a description of the underlying molecules is needed. What, then, are the underlying degrees of freedom of M-theory?
Banks, Fischler, Shenker and Susskind (BFSS) conjectured that Matrix theory could provide the answer. They demonstrated that a theory of 9 very large matrices, evolving in time, could reproduce the Super gravity description at low energy, but take over for it as it breaks down at high energy. While the Super gravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, non-commutative geometry takes over, somewhat similar to the way the continuum of water breaks down at short distances in favor of the graininess of molecules.
Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by N. Ishibashi, H. Kawai, Y. Kitazawa, and A. Tsuchiya.
There is a duality theory called mysterious duality relating M-theory and the geometry of del Pezzo surfaces.
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Abbreviation of membrane.
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Singular |
Plural |
M-theory (uncountable)
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M-theory is a new idea in small-particle physics that is part of superstring theory. The idea, or theory, often causes arguments among scientists, because there is no way to test it to see if it is true. If ever proven true, M-theory and string theory would mean big progress for science.
To understand M-theory one must first have some knowledge of string theory. For hundreds of years scientists have thought that the simplest objects in the universe are points, like dots. String theory says that this is wrong and that the simplest objects in the universe are shaped like pieces of string. These strings are so small that even when looked at very closely they look like points. Each basic particle is created by the strings vibrating in different patterns. The reason scientists had not thought of this idea for so long is that strings are much harder to work with than points. They seem to break such rules as causality and special relativity, which says that information cannot travel faster than the speed of light.
String theory has been developed because of a very important problem that has existed for almost 100 years. Albert Einstein's theory that describes the universe on very large scales (it is called general relativity), disagrees with two theories that describe things on very small scales (they are called quantum mechanics and the standard model). There are also problems with the Standard Model: it includes about 20 numbers that seem to have no explanation; it has too many basic particles - some scientists think it needs to have fewer; and it does not include gravity, which is needed to explain weight.
Many of these problems can be solved by thinking of basic particles as strings. Now there is only one number with no explanation, which gives the size of the strings. String theory includes particles that cause gravity, called gravitons; finding this out delighted the scientists who work on string theory. So, string theory successfully brings General Relativity and Quantum Mechanics together.
But there are some problems with string theory. Normally, we think of the universe as having 4 dimensions, or basic directions. 3 of these basic directions can be thought of as "up/down", "forward/backward" and "left/right". The other direction is time. String theory needs 10 basic directions.
These six other directions can be explained if they are "curled up", so they are much too small to see. For example, by following the path of a spiral, it is possible to go a great distance along it without moving very far. The 6 other directions can be thought of as tiny spirals - strings can move along them a great distance but not seem to move. This can be looked at as a mathematical trick -- a trick that has little to do with the real world that can be seen and touched. Such tricks are allowed if they give a theory that can better tell us how things work.
Another problem with string theory is that there are 5 different versions of it. Each version allows different kinds of strings and says they work in different ways. String theory is supposed to be a theory of everything so there should be only one version, not 5. M-theory solves this problem.
In 1995 Edward Witten started what has been called the Second Superstring Revolution by introducing M-theory to the world. This theory combines the 5 different string theories (along with a previously abandoned attempt to unify General Relativity and Quantum Mechanics called 11D-Supergravity) into one theory. What Witten actually did was to predict that the fact that all these different theories were connected was a result of there being some underlying theory of which they were all approximations. This theory is somewhat vague in nature and has not yet been pinned down.
Additionally, it was found that the equations that required string theory to exist in 10 dimensions were actually approximations as well. The proposed M-theory would need one extra dimension and instead be a theory that takes place in 11 dimensions. Witten has himself compared this idea in simple terms to a general who takes up a position on a hilltop, the extra space-coordinate, to get a better view of the battlefield's two other dimensions.
The combination is accomplished by knitting together a web of relationships between each of the string theories called dualities (specifically, S-duality, T-duality, and U-duality). Each of these dualities provides a way of converting one of the string theories into another. T-duality is probably the most easily explained of the dualities. It has to do with the size, written as R, of the curled up dimensions of the string theories. It was discovered that by taking a Type IIA string theory that has a size R and changing the radius to 1/R the result will end up being what is equivalent to a Type IIB theory of size R. This duality, along with the others, creates connections between all 5 (or 6, if supergravity is counted) theories. The fact that these dualities existed had been known before Witten came up with the idea of M-theory.
Additional amusement has come for many in guessing what the M might stand for (possibilities include Matrix, Magic, Muffin, Mystery, Mother and Membrane). Regardless of what the M might possibly mean, M-theory has become one of the most interesting and active areas of research in theoretical physics today.
For a more technical explanation, see w:M-theory (simplified explanation).
   | M-Theory-Cambridge - M-theory, the theory formerly known as Strings |
| | M-Theory (the Theory Formerly Known as Strings) - [hep-th/9608117] M-Theory (the Theory Formerly Known as Strings) |
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