String theory

Superstring theory

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In physics, M-theory is a proposal that unifies the five ten-dimensional superstring theories as limits of a single 11-dimensional theory. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. See also String theory Superstring theory is an attempt to explain all of the particles and Fundamental forces of nature in one theory by modelling Though a full description of the theory is not yet known, the low-energy dynamics are known to be supergravity interacting with 2- and 5-dimensional membranes. In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity This theory is the unique supersymmetric theory in eleven dimensions, with its low-energy matter content and interactions fully determined. In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that

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. For the Indian Politician, see Ashoke Kumar Sen. Ashoke Sen (অশোক সেন (born 1956 is among India's This article is about Physicist and string theorist Michael Duff John Henry Schwarz (born 1941) is an American theoretical physicist. Edward Witten (born August 26, 1951) is an American Theoretical physicist and Professor at the Institute for Advanced Study The Institute for Advanced Study, located in Princeton New Jersey, United States is a center for theoretical research The University of Southern California (commonly referred to as USC, SC, Southern California, and incorrectly String duality is a class of symmetries in Physics that link different string theories, theories which assume that the fundamental building blocks of the The second superstring revolution was the intense wave of breakthroughs in String theory that took place approximately between 1994 and 1997.

According to Witten and others, the M in M-theory could stand for master, mathematical, mother, mystery, membrane, magic, or matrix. Witten reluctantly admits the M in M-theory can also stand for murky due to the fact that the level of understanding of the theory is so primitive. ^[1]

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".

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. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric A Dynamical Theory of the Electromagnetic Field which was written in the year 1864 is the third of James Clerk Maxwell 's papers concerned with Electromagnetism 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, Lie 3-Algebras. In Mathematics, associativity is a property that a Binary operation can have In Mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable Manifolds Lie Practitioners hope the Bagger-Lambert-Gustavsson action (BLG action) will provide the long-sought microscopic description of M-theory.

Contents 1 History and Development 1.1 Prior to May 1995 1.2 Type I string theory and others 1.3 String vibrational patterns 1.4 M-theory 1.5 Type IIA and Type IIB 1.6 Other dualities 1.7 Only two string theories 1.8 Last step 1.9 Supergravity theories 1.10 Same underlying theory 2 Nomenclature 3 M-theory and membranes 3.1 P-branes 3.2 Strings with "loose ends" 3.3 Strings with closed loops 4 Membrane Interactions 5 Matrix theory 5.1 Analogy with water 5.2 9 matrices 6 See also 7 References 8 Books 9 External links

History and Development

Prior to May 1995

Prior to 1995 there were five (known) 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. In Theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions In Theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. In Theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In Mathematics, the orthogonal group of degree n over a field F (written as O( n, F) is the group of n 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. The Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1 Calculations have also shown that each theory requires more than the normal four spacetime dimensions (although all extra dimensions are in fact spatial. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS ) However, when the theories are analyzed in detail, significant differences appear.

Type I string theory and others

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 D-branes, that is to say, they are tight). In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named

String vibrational patterns

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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Attempts by the physics community to eliminate four of the theories, leaving only one string theory, have not been successful.

M-theory

M-theory attempts to unify the five string theories by examining certain identifications and dualities. Thus each of the five string theories becomes a special case 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.

Type IIA and Type IIB

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. T-duality is a symmetry between small and large distances that is not present in Kaluza-Klein compactification of a Particle theory.

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.

Other dualities

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. In Physics, a heterotic string is a peculiar mixture (or hybrid of the bosonic string and the Superstring (the adjective heterotic comes from In Mathematics, the orthogonal group of degree n over a field F (written as O( n, F) is the group of n 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. In theoretical Physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and 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.

Only two string theories

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.

Last step

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. In quantum field theory (QFT the forces between particles are mediated by other particles 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. In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory. In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity

Supergravity theories

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.

Same underlying theory

M-theory would implement the notion that all of the different string theories are different special cases and/or different presentations of the same underlying theory (M-theory). Thus the concept of string theory is expanded. Unfortunately little is known about M-theory, but there is a great deal of interest in the concept from the theoretical physics community. Computations in M-theory and string theory in general are extremely complex, so concrete results are very difficult to produce. It may be some time before the full implications of these theories are known.

The promise of M-theory is that all of the different string theories would become different limits of a single underlying theory.

Nomenclature

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. "^[2] According to the BBC/TLC documentary Parallel Universes, the M stands for "membrane". TLC (generally called as The Learning Channel) is a cable TV network in the US and Canada, that carries a variety of informational and Other suggestions by people such as Michio Kaku, Michael Duff and Neil Turok in that documentary are "mother" (as in "mother of all theories"), and "master" theory. Dr Michio Kaku (b January 24, 1947) is an American theoretical physicist specializing in String field theory, and a Futurist This article is about Physicist and string theorist Michael Duff Neil Geoffrey Turok holds the Chair of Mathematical Physics (1967 at Cambridge University. ^[3]

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^[4]. 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 Elegant Universe Superstrings Hidden Dimensions and the Quest for the Ultimate Theory (ISBN 0-375-70811-1 is a Book by Brian Greene published in

• 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. For the Indian Politician, see Ashoke Kumar Sen. Ashoke Sen (অশোক সেন (born 1956 is among India's Ur ( Sumerian:urim; Akkadian: ?) is modern Tell el-Mukayyar, Iraq, and was a city in ancient Sumer. Über or ueber ( comes from the German language. It is a Cognate of both Latin super and Greek ὑπέρ ( hyper) as well as (It might also stand for U-duality, which is both a reference to Sen's own work and a kind of particle physics pun. U-duality is a symmetry of String theory or M-theory combining S-duality and T-duality transformations )

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

In the standard string theories, strings are assumed to be the single fundamental constituent of the universe. M-theory adds another fundamental constituent - membranes. In Theoretical physics, a membrane, brane, or p -brane is a spatially extended mathematical concept that appears in String theory Like the tenth spatial dimension, the approximate equations in the original five superstring models proved too weak to reveal membranes.

P-branes

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. In Theoretical physics, a membrane, brane, or p -brane is a spatially extended mathematical concept that appears in String theory 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.

Strings with "loose ends"

Shortly after Witten's breakthrough in 1995, Joseph Polchinski of the University of California, Santa Barbara discovered a fairly obscure feature of string theory. Joseph Polchinski (born on May 16, 1954 in White Plains, New York) is a Physicist working on String theory. The University of California Santa Barbara ( UCSB) is a selective research-oriented public university located on the Pacific Ocean in Santa Barbara County California 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. In String theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions after which they are named 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.

Strings with closed loops

Not all strings are confined to p-branes. Strings with closed loops, like the graviton, are completely free to move from membrane to membrane. In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework Of the four force carrier particles, the graviton is unique in this way. In Physics, the graviton is a hypothetical Elementary particle, a Boson to be exact that mediates the force of Gravity in the framework 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. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and In Physics, the electromagnetic force is the force that the Electromagnetic field exerts on electrically charged particles 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. Gravitation is a natural Phenomenon by which objects with Mass attract one another

Membrane Interactions

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. KNOT (1450 AM) is a commercial Classic Country music Radio station in Prescott Arizona, broadcasting to the Flagstaff - Prescott In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces Since M-Theory is thought to live in 11 dimensions then this problem gets 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. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of The basic orientable 2-brane interactions are easy to show. A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back Orientable 2-branes are multi-holed tori with multiple holes cut out of them.

Matrix theory

The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Supergravity. In Theoretical physics, supergravity ( supergravity theory) is a field theory that combines the principles of Supersymmetry and General relativity 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.

Analogy with water

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?

9 matrices

Banks, Fischler, Shenker and Susskind (BFSS) conjectured that Matrix theory could provide the answer. Tom Banks is a theoretical physicist at University of California Santa Cruz and a professor at Rutgers University. Willy Fischler born in 1949 in Antwerpen, Belgium is a theoretical physicist and string theorist. Leonard Susskind (born 1940 is the Felix Bloch professor of Theoretical physics at Stanford University in the field of String theory and In Physics, matrix string theory is the first known set of equations that describe Superstring theory in a non-perturbatively complete and consistent framework 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. Noncommutative geometry, or NCG, is a branch of Mathematics concerned with the possible spatial interpretations of Algebraic structures for which the

See also

• AdS/CFT correspondence

References

Books

• Brian Greene has written books explaining string theory and M-theory for the layperson in 1999, The Elegant Universe, ISBN 0-375-70811-1 and in 2004, The Fabric of the Cosmos, ISBN 0-375-41288-3. Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. The Elegant Universe Superstrings Hidden Dimensions and the Quest for the Ultimate Theory (ISBN 0-375-70811-1 is a Book by Brian Greene published in The Fabric of the Cosmos: Space Time and the Texture of Reality ( 2004) is the second book on Theoretical physics,
• Kaku, Michio (1999). Strings, Conformal Fields, and M-Theory. New York: Springer. ISBN 0387988920.   for a more advanced introduction.

External links

• The Elegant Universe - A Three-Hour Miniseries with Brian Greene by NOVA (original PBS Broadcast Dates: October 28, 8-10 p. Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. m. and November 4, 8-9 p. m. , 2003). Various images, texts, videos and animations explaining string theory and M-theory.
• Superstringtheory.com - The "Official String Theory Web Site", created by Patricia Schwarz. Excellent references on string theory and M-theory for the layperson and expert.
• Basics of M-Theory by A. Miemiec and I. Schnakenburg is a lecture note on M-Theory published in Fortsch. Phys. 54:5-72,2006.
• M-Theory-Cambridge
• M-Theory-Caltech
• The Elegant Universe – A Three-Hour Miniseries with Brian Greene by NOVA. Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists.

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