The theory of the cords is one of the ways planned to regulate one of the major questions of the Theoretical physics: to provide a description of the quantum Revolved i.e. unification of the quantum Mechanical (inevitable to describe physics with the small scales) and theory of the General relativity (necessary to describe the Relativistic Gravitation in manner ).

The principal characteristic of the theory of the cords is that its ambition does not stop with this reconciliation, but that she claims to succeed in unifying the four elementary interactions known, one speaks about Théorie of the whole.

Overflight of the theory

Bases

The theory rests on two rather revolutionary assumptions:

• the fundamental bricks of the Universe would not be specific particles but kinds of vibrating cords having a tension with the manner of an elastic . What we perceive like particles distinct characteristics (Masse, electric Charge, etc) would be only cords vibrating differently. With this assumption, the theories of the cords admit a minimal scale, connected to the Taille of Planck, and thus make it possible to easily avoid the appearance of certain infinite quantities (one speaks about “divergences”) which are inevitable in the quantum theories of usual fields.
• the Univers would contain more than three space dimensions . Some of them, folded up on themselves (see the theories of Oskar Klein), passing unperceived on our scales (by a procedure called dimensional Reduction).

Elements supporting the theory

The theory of the cords obtained first very promising partial results. Within the framework of the Thermodynamique of the black holes it makes it possible to reproduce the formula of Bekenstein and Hawking for the Entropie of the black holes. It also has a remarkable mathematical richness: in particular, it made it possible to discover the Symétrie mirror in Géométrie.

Weaknesses of the theory

However the theory of the cords remains incomplete. On the one hand, a multitude of solutions to the equations of the theory of the cords exists, which poses a problem of selection of our universe and, on the other hand, even if many close models could be obtained, none of them does not allow to give an account of the standard model precisely of the physics of the particles.

Although various independent formulations (cf below) were developed in the years 1980, the results of Dualité of cords obtained in years 1990 made it possible to consider that all the theories previously built are themselves only various limits of a more fundamental single theory, baptized Théorie M, whose microscopic formulation remains unknown but whose effective Théorie basic energy is the maximum Supergravité with 11 dimensions, that is to say one moreover than the Dimension criticizes theories of supercordes.

History of the theory

See also: History of the theory of the cords

Genesis, a first unfruitful attempt

The theory of the cords was initially introduced as attempt at description of the strong Interaction but its predictions were in disagreement with the experimental observations. It was thus quickly abandoned with the profit of the quantum Chromodynamique (shortened in QCD).

The first revolution of the cords

See also: First revolution of the cords

In 1984, by a remarkable technical prowess, Michael B. Green and John H. Schwarz show the absence of anomalies of gravitational gauge or in the theory of cords of the type I which is a chiral Théorie just as the standard model. This work offers for the first time the prospect to obtain a realistic Phénoménologie starting from cords. The impact was so important in the community of the theoretical physics that the term of revolution was adopted to describe the very fast period of development which was followed from there.

The second revolution of the cords

See also: Second revolution of the cords

In the middle of the years 1990, a great number of bridges or dualities is discovered between the various theories of cords. In 1995 the physicist Edward Witten suggests that these dualities are the counterpart of the existence of a more fundamental theory, called Théorie M continuously joining together the various theories of the cords which are then obtained in some limiting of its space of the parameters (called Espace of modules). This period of intense activity in the field was worth the name of to him second revolution of the cords .

Current developments

Several physicists endeavor to develop the theory of the cords, supposed to unify the four great forces which govern the Univers.

The AdS/CFT correspondence

See also: Correspondence AdS/CFT

In 1997, Juan Maldacena proposes a conjecture, called Correspondance AdS/CFT which affirm, in its most general form, complete equivalence between some Théorie of gauge, the Théorie of super Yang-Millets with wide supersymmetry $N=4$ and the theory of the cords of the IIb type about space $AdS\_5\; \backslash \; times\; S\_5$.

To date (2006) the AdS/CFT correspondence was not shown but a very great number of very not-commonplace tests were carried out where the conjecture was always checked with a high degree of accuracy. These tests consist most of the time of two calculations carried out independently within the framework of the theory of gauge on the one hand and within the framework of the theory of the cords on the other hand and in a comparison of the two results.

This conjecture is remarkable insofar as it establishes a natural relation between a theory of gauge, by not-gravitational nature , and a theory of quantum gravity what goes in the direction of an intuition formulated for a long time by the physicist Gerald 'T Hooft.

In addition the AdS/CFT correspondence constitutes a realization of the holographic Principe insofar as the space on which the theory of super-Yang Millets lives is located at the edge space $AdS\_5\; \backslash \; times\; S\_5$ on which is defined the IIb theory. As this space corresponds to the effective geometry in the vicinity of the horizon of some black holes, the AdS/CFT correspondence can be used to analyze in detail the entropy of this type of black holes.

Geometrical transitions

See also: geometrical Transition

Inspired by successes of the AdS/CFT conjecture but in front of the difficulty of showing the latter, a certain number of work were initiated succeed with equivalences between topological theories of gauge, intrinsically simpler than the theory of super Yang-Millets, and models of Théorie of the topological cords, them as simpler as the theories of the usual supercordes.

One of the most known examples of such an equivalence is the geometrical transition from Gopakumar/Vafa during which the Théorie of Chern-Simons with group of gauge $SU\; (NR)$ formulated on the sphere with three dimensions $S\_3$ is equivalent within the limit $N\; \backslash \; rightarrow\; \backslash \; infty$ to the theory of the topological cords of type has on the solved conifold which is a Espace of Calabi-Yau mathematically noted $O\; (-\; 1)\; \backslash \; oplus\; O\; (-\; 1)/\backslash \; mathbb\; \{P\}\; \_1$.

The topological misadventures of the AdS/CFT correspondence have two practical advantages compared to the latter

• On the one hand they are relatively simpler to prove: the theories of topological cords being naturally connected to the evaluation of topological invariants of spaces on which they are formulated, the predictions resulting from the topological theory of gauge can be subjected to a meticulous analysis on behalf of the mathematicians.
• In addition, a certain number of work could show that some Observable S of the effective theories of the standard theories of supercordes can be calculated by using topological theories of cord. In this manner it is then possible to carry out a relation between a topological theory of gauge and a theory of standard gauge. A famous example is the correspondence of Dijkgraaf/Vafa which establishes this manner a relation between the effective theory non-perturbative of a supersymmetric theory of Yangs-Millets $N=1$ and a theory of random matrices. The correspondence, which with final is formulated only in one context of theories of gauge, could be thereafter shown completely by using only the tools of the Quantum theory of the fields. This last example illustrates how the theory of the cords could be useful from a formal point of view for the comprehension of the aspects non-perturbatifs of the theories of gauges when well even it could fail from a phenomenologic point of view to describe our universe.

The Landscape

The theories of the cords admit a great number of solutions to their equations which are as many coherent universes from the point of view of these theories. Vis-a-vis this multitude, two positions exist in the community of the scientists working in this field

• the orthodoxe position consists in considering that this multitude poses a problem of predictivity of the theory. Nevertheless this multitude would result from a lack of control on the phenomena non-perturbatifs existing in the theory and that a better comprehension of those should lead to the natural elimination of a great number of solution to let emerge ultimately only some models in agreement with the current observations.
• a new point of view, initiated by work of Michael Douglas considers that it is possible that intrinsically the theory of the cords admits a great number of distinct solutions but that in this whole of unquestionable solutions characteristic generic are statistically more probable. For example, a great number of work seek to determine if the weakness of the cosmological Constante is statistically supported, or if the Groupe of gauge $SU\; (3)\; \backslash \; times\; KNOWN\; (2)\; \backslash \; times\; U\; (1)\; \backslash ,$ of the standard model would be privileged compared to groups of gauge of higher size. The principal criticism formulated by the orthodoxe current against this position relates to the difficulty of defining a Loi of probability on the unit of the solutions in the absence of principle physically justified first.

Various theories of the cords

There exist several theories of the cords:

• the bosonic theory of the cords with 26 dimensions. It is the original theory of the cords and simplest. The formulation of the theory on its sheet of universe contains only Bosons from where its name. It contains a Tachyon (hypothetical particle whose energy is measured by a pure Imaginary number and masses it, by a Real number), which is an indication which the theory is unstable, and thus unsuitable describing reality. It is however useful pedagogically to be familiarized with the fundamental concepts which one finds in more realistic models. In particular on the level of null mass it reveals the Graviton. She admits open or closed cords.
• Five theories of the supercordes with 10 dimensions, which do not have Tachyon S and which suppose the existence of a Supersymétrie on the Feuille of universe of the cords lead to the existence of supersymmetries in the Space-target:
• I : open or closed cords, group of symmetry SO (32)
• IIA : only closed cords, non-chirality
• IIB : only closed cords, chirality
• HO : only closed cords, heterodicity, group of symmetry SO (32)
• HE : only closed cords, heterodicity, group of symmetry E₈×E₈
• the Theory M, result of these theories

The theories of the supercordes are distinguished from the first by the existence of an additional symmetry, the Supersymétrie, which proved to be necessary when one wished to incorporate the fermions (matter) in the bosonic theory of the cords.

It would seem that these five theories are various limits of a theory still badly known, resting on a space with 11 dimensions (10 space and temporal), called Théorie M, which would admit the maximum Supergravité developed in the years 1970 like effective Théorie basic energy. This assumption was proposed by Horava and Witten in the years 1990 and brought the introduction of other objects extended in addition to the cords. One speaks about p-branes, p being an entirety which indicates the number of space size of the object in question. They are described perturbativement as the subspaces on which the ends of open cords live. The study of the spectrum shows that of D1, D3, D5, D7 and D9 branes can be built-in a Space-target describes by theory IIB while into a space where live of the cords of the type IIA one can introduce branes of the type D0, D2, D4, D6 and D8. Let us note that D1 have the same number of dimensions as a fundamental cord (usually noted F1). Although being two distinct objects, a non-perturbative symmetry of theory IIB, called S-duality, which underwent a big number of indirect checks, has the property to exchange D1 brane with F1.

Branes

See also: Brane

A brane , or more exactly, a p-brane is an object extended in theory of the cords. The p is the number of space size in which the brane has extensions. It is necessary to add with this number a temporal dimension to obtain the full number of dimensions. For example, a 1-brane is a brane with only one space dimension but two dimensions on the whole. They thus correspond to surfaces of universe. A 2-brane is a brane with a temporal dimension and two dimensions space.

Cosmology branaire

See also: Cosmology branaire

Several model cosmological emerged from the introduction of the branes in theory of the cords. The general idea of cosmology branaire is that our universe would be confined on a 4-brane. This means that matter particles (Quark S, electron S, etc…) and fundamental interactions others that gravitation (transported by the particles the such Photon, the Gluon, etc…) are authorized to move only inside the brane while the gravitation with the possibility of also moving in the complete space time (one says also the bulk in English) whose brane represents only one subspace.

In addition within the framework of the model of the Big Bang an idea was introduced recently like alternative to the cosmic Inflation to describe the very first moments of the history of the Univers, the model ekpyrotic. In this model, the initial expansion is due to the collision of a brane and anti-brane, which releases energy necessary to the expansion of the universe. This model predicts the possibility of other collisions what would involve other Big Bang. Nevertheless it did not cause the unanimity within the community of the cosmologists and cosmic inflation remains the mechanism mainly considered to describe the first moments.

Surface universe

See also: Surface of universe

The surface of universe is the surface covered by the movement of a cord. It is, more exactly, a 1-brane.

Additional dimensions

See also: Theory of Kaluza-Klein, dimensional Reduction, rolled up Dimensions

According to the theory of the cords, our world, apparently three-dimensional, not would consist of three space dimensions, but of 10,11, or even 26 dimensions. Without these additional dimensions, the theory collapses. Indeed, mathematical coherence imposes the presence of additional dimensions. The reason for which they remain invisible, is that they would be rolled up by the process of the dimensional Réduction has a microscopic scale (billion times smaller than an atom!!), which would not enable us to detect them.

Indeed, if one imagines a cable considering by far, that Ci represents only one line without thickness, a unidimensional object. If one approaches enough close, one realizes that there is the second dimension well, that which is surrounded around the cable! According to the theory of the cords, the space fabric could even have very great dimensions like our three usual but also low-size dimensions rolled up on them.

Spaces of Calabi-Yau

See also: Space of Calabi-Yau

Spaces of Calabi-Yau are varieties which play the part of dimension rolled up. It is an extremely complex form made up with it only of six dimensions. Thanks to them, one finds oneself well with ten dimensions: our four usual dimensions + six of spaces of Calabi-Yau.

Theory M

See also: Theory M

The theory M, allied with the supergravity with eleven dimensions, is the result of the five theories of the cords. She was discovered by Edward Witten, in 1995. At the time of the conference Strings' 95 , it showed that if one raised the constant coupling cord Hétérotique E, of a negative number, at a positive number, that highlighted the supergravity. The origin of the name of the Theory M is rather dubious, and gives place to jokes.

The constant of coupling of the cords

See also: Coupling in theory of the cords

In theory of the cords, the constant of coupling is a positive number which determines the probability with which two cords can be melted in one, then Re-to separate. It is thanks to this concept that the Théorie M was discovered.

Supersymmetry

See also: Supersymmetry

The supersymmetry is a symmetry in Physique particles. It establishes a very solid bond between the particles equipped with a whole Spin, and those equipped with a spin half-entirety. In this context, the Fermion S are associated with another type of particle: the Superpartenaire . The superpartenaires are large particles in any point identical to their associated , except on the level of the spin: that of the superpartenaire differs from a half-unit.

Supergravity

See also: Supergravité

The supergravity is a theory which combines the supersymmetry with the General relativity. Its operation is thus based on 11 dimensions.

Predictions of the theories of the cords

• the Graviton, boson (i.e mediator) of the Gravitation would be a particle of Spin 2 and null mass (in accordance with the quantum physics). Its cord has an amplitude of null waves.
• It does not have there measurable differences between cords which are rolled up around a dimension and those which move in dimensions (i.e., the effects in a dimension of size R are the same ones as in a dimension of size 1/R).

Limitations and controversies concerning the theories of the cords

The theory of the cords caused, and still causes, much hopes. However a certain number of important points seem to pose problem and always are very discussed. None of these controversies invalidates the theory definitively, but they show that this theory still needs to evolve/move, to improve and correct its weaknesses.

• Not prediction and difficulties of interpretation of the black energy .

One of the major experimental facts observed these last years is that the universe is in accelerated expansion. A black energy, of unknown nature, was postulated to explain this acceleration. This black energy can be also seen like a cosmological Constante positive. The theory of the cords did not envisage the acceleration of the expansion of the universe because this theory naturally leads worms of the universes to negative or null cosmological constant. To make the theory of the cords compatible with a positive constant proved very difficult and was carried out only in 2003 by a group of the university of Stanford. But one of the consequences of this work is that there exists about $10^\; \{500\}$ theories of the possible cords, giving a " paysage" (landscape) of theories rather than a single theory. The existence of this enormous number of different theories - which have all the same theoretical validity - leads directly to the assumption of a Multivers, even with the Principe anthropic, which gene or intrigue many physicists.

Joseph Polchinski observes however that Steven Weinberg predicted in the years 1980 a not-null constant cosmological by making the assumption of a Multivers, which is precisely a possible consequence of the theory of the cords.

• Irréfutabilité and absence of predictions

According to Peter Woit, a theory of the cords cannot even be false . Indeed, the Landscape of theories makes it possible to adjust the free constants of the theory of the cords so as to put up with practically any observation, known or to come. For example, if LHC does not detect the particles Superpartenaire S, it will be possible to modify the theory to make these particles heavier in order to explain their not-detection. This flexibility also makes very difficult to make physical predictions of phenomena being able to test and validate the theory of the cords. Moreover, one does not know if it will be possible to carry out experiments on additional dimensions of the Universe.

If the theory of the cords is not easily refutable, it can however be verifiable. Recently, of the assumptions were worked out to check the theory of the cords.

• Independence of the basic geometry

The theory of the cords is currently described like a Semi-traditional theory . I.e. considering an environment (basic geometry plus possible matter) fixed, the formulation as model sigma makes it possible to find and study the energizations of the cords only in the vicinity of this geometry. An analog in quantum mechanics of this situation is the study of the Atome of hydrogen bathing in a basic electric field (what makes it possible for example to study the spontaneous emission but not stimulated).

A certain number of points are however to note:

- invariance by diffeomorphisms of target space belongs to symmetries of the theory.

- For the quantum consistency of the theory, the environment must satisfy the equations of general relativity.

- Among the energizations of the cord one finds a particle, the graviton, which has the quantum numbers necessary to the description of metric general as coherent state of revolve.

- the states of the theory are functions of wave corresponding to a number fixed of cords.

The first two points show that the theory is perfectly compatible with general relativity. The second point is similar in the case of the hydrogen atom with the need for the basic field for satisfying the Maxwell's equations. In order to release itself from these constraints on the environment, and by analogy with the Second quantification in the case of the particles which ends in the Quantum theory of the fields, it is thus desirable to have a Théorie of fields of cords which corresponds to the quantification of these functions of waves of cords. This formulation exists but the technical complications due to the wide nature of the cords mathematically return the research solution exact to its equations extremely difficult, and thus its impact on the developments in theory of the cords is still limited by comparison to the impact which the quantum theory of the fields in physics of the particles had.

Let us note finally that in quantum Gravitation with loops which is another candidate for a quantum description of the gravity (but which does not make it possible to incorporate matter fields however) the formulation of the theory is explicitly independent of the basic geometry but it is not established yet that it respects the Invariance of Lorentz.

• Finitude of the theory not formally shown .

The theory of the cords is often presented like having solved the problem of the " infinies" quantities;, which appears in the Quantum theory of the fields or in the General relativity. This is a major success of the theory of the cords, and the exactitude of its demonstration is thus an important issue. A proof was published in 1992 by Stanley Mandelstam that certain types of divergences do not appear in the equations the theory of the cords. However, as Mandelstam grants it itself in a letter to Carlo Rovelli, it is not excluded that other types of infinite can apparaître.
In 2001, Eric D' Hoker and Duong H. Phong showed that any form of infinite was impossible until order 2 of approximation.
In 2004, Nathan Berkovits manages to show that any form of infinite is impossible, and that with any order of approximation, but by reformulating the theory of the cords, in particular by adding a certain number of presupposed supplémentaires.
In spite of the absence of formal evidence, little of theorists give in doubt the finitude of the theory of the cords. But some, as Lee Smolin thinks that the difficulty of leading to a final proof testifies to fundamental problems on this level.

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