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Superstring theory is anattempt to explain all of theparticles andfundamental forces of nature in one theory by modeling them as vibrations of tinysupersymmetricstrings.
'Superstring theory' is a shorthand forsupersymmetric string theory because unlikebosonic string theory, it is the version ofstring theory that accounts for bothfermions andbosons and incorporatessupersymmetry to model gravity.
Since thesecond superstring revolution, the five superstring theories (Type I,Type IIA,Type IIB,HO and HE) are regarded as different limits of a single theory tentatively calledM-theory.
One of the deepest open problems intheoretical physics is formulating a theory ofquantum gravity. Such a theory incorporates both the theory ofgeneral relativity, which describes gravitation and applies to large-scale structures, andquantum mechanics or more specificallyquantum field theory, which describes the other threefundamental forces that act on the atomic scale.
Quantum field theory, in particular theStandard Model, is currently the most successful theory to describe fundamental forces, but while computing physical quantities of interest, naïvely one obtains infinite values. Physicists developed the technique ofrenormalization to 'eliminate these infinities' to obtain finite values which can be experimentally tested. This technique works for three of the four fundamental forces:Electromagnetism, thestrong force and theweak force, but does not work forgravity, which is non-renormalizable. Development of aquantum theory of gravity therefore requires different means than those used for the other forces.[1]
According to superstring theory, or more generally string theory, the fundamental constituents of reality are strings with radius on the order of thePlanck length (about 10−33 cm). An appealing feature of string theory is that fundamental particles can be viewed as excitations of the string. The tension in a string is on the order of thePlanck force (1044newtons). Thegraviton (the proposedmessenger particle of the gravitational force) is predicted by the theory to be a string with wave amplitude zero.
Investigating how a string theory may include fermions in its spectrum led to the invention ofsupersymmetry (inthe West[clarification needed])[2] in 1971,[3] a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as "superstring theories".
Since its beginnings in the seventies and through the combined efforts of many different researchers, superstring theory has developed into a broad and varied subject with connections toquantum gravity,particle andcondensed matter physics,cosmology, andpure mathematics.
Superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and initial investigation, carried out in 2011 at theLarge Hadron Collider (LHC)[4] and in 2006 at theTevatron has excluded some of the ranges.[5][self-published source?][6][7][8] For instance, the mass constraint of theMinimal Supersymmetric Standard Modelsquarks has been up to 1.1 TeV, andgluinos up to 500 GeV.[9] No report on suggestinglarge extra dimensions has been delivered from the LHC. There have been no principles so far to limit the number of vacua in the concept of a landscape of vacua.[10]
Some particle physicists became disappointed by the lack of experimental verification of supersymmetry, and some have already discarded it.[11]Jon Butterworth atUniversity College London said that we had no sign of supersymmetry, even in higher energy regions, excluding thesuperpartners of the top quark up to a few TeV. Ben Allanach at the University of Cambridge states that if we do not discover any new particles in the next trial at the LHC, then we can say it is unlikely to discover supersymmetry atCERN in the foreseeable future.[11]
Ourphysical space is observed to havethree large spatialdimensions and, along withtime, is a boundless 4-dimensionalcontinuum known asspacetime. However, nothing prevents a theory from including more than 4 dimensions. In the case ofstring theory,consistency requires spacetime to have 10 dimensions (3D regular space + 1 time(1 time dimension is not necessary, it may be multi-dimensional, according to F-theory[12]) + 6Dhyperspace).[13] The fact that we see only 3 dimensions of space can be explained by one of two mechanisms: either the extra dimensions arecompactified on a very small scale, or else our world may live on a 3-dimensionalsubmanifold corresponding to abrane, on which all known particles besides gravity would be restricted.
If the extra dimensions are compactified, then the extra six dimensions must be in the form of aCalabi–Yau manifold. Within the more complete framework of M-theory, they would have to take form of aG2 manifold. A particular exact symmetry of string/M-theory calledT-duality (which exchanges momentum modes forwinding number and sends compact dimensions of radius R to radius 1/R),[14] has led to the discovery of equivalences between different Calabi–Yau manifolds calledmirror symmetry.
Superstring theory is not the first theory to propose extra spatial dimensions. It can be seen as building upon theKaluza–Klein theory, which proposed a 4+1 dimensional (5D) theory of gravity. When compactified on a circle, the gravity in the extra dimension precisely describeselectromagnetism from the perspective of the 3 remaining large space dimensions. Thus the original Kaluza–Klein theory is a prototype for the unification of gauge and gravity interactions, at least at the classical level, however it is known to be insufficient to describe nature for a variety of reasons (missing weak and strong forces, lack ofparity violation, etc.) A more complex compact geometry is needed to reproduce the known gauge forces. Also, to obtain a consistent, fundamental, quantum theory requires the upgrade to string theory, not just the extra dimensions.
Theoretical physicists were troubled by the existence of five separate superstring theories. A possible solution for this dilemma was suggested at the beginning of what is called thesecond superstring revolution in the 1990s, which suggests that the five string theories might be different limits of a single underlying theory, called M-theory. This remains aconjecture.[15]
| String theories | |||||||
|---|---|---|---|---|---|---|---|
| Type | Spacetime dimensions | SUSY generators | chiral | open strings | heterotic compactification | gauge group | tachyon |
| Bosonic (closed) | 26 | N = 0 | no | no | no | none | yes |
| Bosonic (open) | 26 | N = 0 | no | yes | no | U(1) | yes |
| I | 10 | N = (1,0) | yes | yes | no | SO(32) | no |
| IIA | 10 | N = (1,1) | no | no | no | U(1) | no |
| IIB | 10 | N = (2,0) | yes | no | no | none | no |
| HO | 10 | N = (1,0) | yes | no | yes | SO(32) | no |
| HE | 10 | N = (1,0) | yes | no | yes | E8 × E8 | no |
| M-theory | 11 | N = 1 | no | no | no | none | no |
The five consistent superstring theories are:
Chiralgauge theories can be inconsistent due toanomalies. This happens when certain one-loopFeynman diagrams cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via theGreen–Schwarz mechanism.
Even though there are only five superstring theories, making detailed predictions for real experiments requires information about exactly what physical configuration the theory is in. This considerably complicates efforts to test string theory because there is an astronomically high number—10500 or more—of configurations that meet some of the basic requirements to be consistent with our world. Along with the extreme remoteness of the Planck scale, this is the other major reason it is hard to test superstring theory.
Another approach to the number of superstring theories refers to themathematical structure calledcomposition algebra. In the findings ofabstract algebra there are just seven composition algebras over thefield ofreal numbers. In 1990 physicists R. Foot and G.C. Joshi in Australia stated that "the seven classical superstring theories are in one-to-one correspondence to the seven composition algebras".[16]
General relativity typically deals with situations involving large mass objects in fairly large regions ofspacetime (when it is applied to small distances it often conflicts with quantum mechanics) whereasquantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case that combines them is in the study ofblack holes. Havingpeak density, or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony to predict conditions in such places. Yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.
The major problem with their incongruence is that, atPlanck scale (a fundamental small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, which are nowhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with strings. These strings have an average diameter of thePlanck length, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping. Also, these surfaces can be mapped as branes. These branes can be viewed as objects with a morphism between them. In this case, the morphism will be the state of a string that stretches between brane A and brane B.
Singularities are avoided because the observed consequences of "Big Crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of one string, at which point it would actually begin expanding.
D-branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of aKaluza–Klein compactification of 11D M-theory that contains membranes. Because compactification of a geometric theory produces extravector fields the D-branes can be included in the action by adding an extra U(1) vector field to the string action.
Intype I open string theory, the ends of open strings are always attached to D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge fields would then correspond to the compactification of some higher-dimensional theory above 11 dimensions, which is not thought to be possible to date. Furthermore, the tachyons attached to the D-branes show the instability of those D-branes with respect to the annihilation. The tachyon total energy is (or reflects) the total energy of the D-branes.
For a 10 dimensional supersymmetric theory we are allowed a 32-component Majorana spinor. This can be decomposed into a pair of 16-component Majorana-Weyl (chiral)spinors. There are then various ways to construct an invariant depending on whether these two spinors have the same or opposite chiralities:
| Superstring model | Invariant |
|---|---|
| Heterotic | |
| IIA | |
| IIB |
The heterotic superstrings come in two types SO(32) and E8×E8 as indicated above and the type I superstrings include open strings.
It is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Because the action for this involves quartic terms and higher so is notGaussian, the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists.Edward Witten has popularised the concept of a theory in 11 dimensions, called M-theory, involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions—which may become acceptable when we find new unknown symmetries of nature, such as noncommutative geometry. It is thought, however, that 16 is probably the maximum since SO(16) is a maximal subgroup of E8, the largest exceptional Lie group, and also is more than large enough to contain theStandard Model. Quartic integrals of the non-functional kind are easier to solve so there is hope for the future. This is the series solution, which is always convergent when a is non-zero and negative:
In the case of membranes the series would correspond to sums of various membrane interactions that are not seen in string theory.
Investigating theories of higher dimensions often involves looking at the 10 dimensional superstring theory and interpreting some of the more obscure results in terms of compactified dimensions. For example,D-branes are seen as compactified membranes from 11D M-theory. Theories of higher dimensions such as 12D F-theory and beyond produce other effects, such as gauge terms higher than U(1). The components of the extra vector fields (A) in the D-brane actions can be thought of as extra coordinates (X) in disguise. However, theknown symmetries includingsupersymmetry currently restrict thespinors to 32-components—which limits the number of dimensions to 11 (or 12 if you include two time dimensions.) Some physicists (e.g.,John Baez et al.) have speculated that the exceptionalLie groups E6, E7 and E8 having maximum orthogonal subgroups SO(10), SO(12) and SO(16) may be related to theories in 10, 12 and 16 dimensions; 10 dimensions corresponding to string theory and the 12 and 16 dimensional theories being yet undiscovered but would be theories based on 3-branes and 7-branes, respectively. However, this is a minority view within the string community. Since E7 is in some sense F4 quaternified and E8 is F4 octonified, the 12 and 16 dimensional theories, if they did exist, may involve thenoncommutative geometry based on thequaternions andoctonions, respectively. From the above discussion, it can be seen that physicists have many ideas for extending superstring theory beyond the current 10 dimensional theory, but so far all have been unsuccessful.
Since strings can have an infinite number of modes, the symmetry used to describe string theory is based on infinite dimensional Lie algebras. SomeKac–Moody algebras that have been considered as symmetries for M-theory have been E10 and E11 and their supersymmetric extensions.
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