# M-theory

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*For a non-technical introduction to the topic, please see Introduction to M-theory.*Template:PhysicsNavigation

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, Jared Farris, Michael Duff, and John H. 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.

## Contents

[show]## Basics Edit

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 *E*_{8}×*E*_{8} (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.

There are other dualities between the other string theories. The heterotic SO(32) and the heterotic *E*_{8}×*E*_{8} 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 *E*_{8}×*E*_{8} 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 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.

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 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 *E*_{8}×*E*_{8} 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.

## Naming conventions, or what does *M* stand for? Edit

There are two issues to be dealt with here:

- When Witten named M-theory, he did not specify what the "M" stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe. According to Witten himself, "'M' stands for 'magic,' 'mystery' , or 'matrix,' according to taste." Other suggestions are 'membrane', 'mother of all theories,' and 'master' theory. 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[1]. 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*.

- 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.

## M-theory and membranes Edit

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 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.

### Matrix theoryEdit

The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Supergravity. 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 Supergravity description is like treating water as a continuous, incompressible fluid. This is great 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 Supergravity description at low energy, but take over for it as it breaks down at high energy. While the Supergravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, noncommutative geometry takes over, somewhat similar to the way the continuum of water breaks down at short distances in favour of the graininess of molecules. Matrix Theory is now understood to be a special case of the celebrated AdS/CFT correspondence.

## Big Bang Edit

Unlike more conventional views of creation in modern physics, that are Ex nihilo, the M-Theory vision, although not yet complete, is of the whole observable universe being one of many extended 4 dimensional branes in an 12 dimensional spacetime. Although branes similar to that representing our universe can co-exist in the theory, their physical laws could differ from our own, as could their number of dimensions. Some proponents of the theory now believe that a collision of two branes may have been responsible for the Big Bang.

## See also Edit

## References Edit

- Banks, T., W. Fischer, S.H. Shenker, L. Suskind (1996). M Theory As A Matrix Model: A Conjecture
- B. de Wit, J. Hoppe, H. Nicolai, "On The Quantum Mechanics Of Supermembranes". Nucl.Phys. B305:545 (1988).
- Duff, Michael J.,
*M-Theory (the Theory Formerly Known as Strings)*, International Journal of Modern Physics A, 11 (1996) 5623-5642, online at Cornell University's arXiv ePrint server [2]. - Gribbin, John.
*The Search for Superstrings, Symmetry, and the Theory of Everything*, ISBN 0-316-32975-4, Little, Brown & Company, 1ST BACK B Edition, August 2000, specifically pages 177-180. - Greene, Brian.
*The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory*, ISBN 0-393-04688-5, W.W. Norton & Company, February 1999 - Kaku, Michio (December 2004).
*Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos*. Doubleday. ISBN 0-385-50986-3, 448. - Taubes, Gary. "String theorists find a Rosetta Stone." Science, v. 285, July 23, 1999: 512-515, 517. Q1.S35
- Witten, Edward. Magic, Mystery and Matrix, Notices of the AMS, October 1998, 1124-1129

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