- Superstring theory
**Superstring theory**is an attempt to explain all of the particles andfundamental force s of nature in one theory by modelling them as vibrations of tiny supersymmetric strings. It is considered one of the most promising candidate theories ofquantum gravity . Superstring theory is a shorthand for**supersymmetric string theory**because unlikebosonic string theory , it is the version ofstring theory that incorporatesfermions andsupersymmetry .**Background**The deepest problem in

theoretical physics is harmonizing the theory ofgeneral relativity , which describes gravitation and applies to large-scale structures (star s,galaxies ,super cluster s), withquantum mechanics , which describes the other threefundamental forces acting on the atomic scale.The development of a

quantum field theory of a force invariably results in infinite (and therefore useless) probabilities. Physicists have developed mathematical techniques (renormalization ) to eliminate these infinities which work for three of the four fundamental forces – electromagnetic, strong nuclear and weak nuclear forces - but not forgravity . The development of aquantum theory of gravity must therefore come about by different means than those used for the other forces.**Basic idea**The basic idea is that the fundamental constituents of reality are strings of the Planck length (about 10

^{−33}cm) which vibrate at resonant frequencies. Every string in theory has a unique resonance, or harmonic. Different harmonics determine different fundamental forces. The tension in a string is on the order of thePlanck force (10^{44}newton s). Thegraviton (the proposed messenger particle of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero. Another key insight provided by the theory is that no measurable differences can be detected between strings that wrap around dimensions smaller than themselves and those that move along larger dimensions (i.e., effects in a dimension of size R equal those whose size is 1/R). Singularities are avoided because the observed consequences of "Big Crunch es" 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 a string, at which point it would actually begin expanding.**Extra dimensions**:"See also: Why does consistency require 10 dimensions?"Our

physical space is observed to have only three largedimension s and—taken together with time as the fourth dimension—a physical theory must take this into account. However, nothing prevents a theory from including more than 4 dimensions, per se. In the case ofstring theory ,consistency requiresspacetime to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified.Our minds have difficulty visualizing higher dimensions because we can only move in three spatial dimensions. One way of dealing with this limitation is not to try to visualize higher dimensions at all, but just to think of them as extra numbers in the equations that describe the way the world works. This opens the question of whether these 'extra numbers' can be investigated directly in any experiment (which must show different results in 1, 2, or 2+1 dimensions to a human scientist). This, in turn, raises the question of whether models that rely on such abstract modelling (and potentially impossibly huge experimental apparatus) can be considered scientific. Six-dimensional

Calabi-Yau shapes can account for the additional dimensions required by superstring theory. The theory states that every point in space (or whatever we had previously considered a point) is in fact a very smallmanifold where each extra dimension has a size on the order of thePlanck length .Superstring theory is not the first theory to propose extra spatial dimensions; the

Kaluza-Klein theory had done so previously. Modern string theory relies on the mathematics of folds, knots, andtopology , which were largely developed after Kaluza and Klein, and has made physical theories relying on extra dimensions much more credible.**Number of superstring theories**Theoretical physicists were troubled by the existence of five separate string theories. This has been solved by the

second superstring revolution in the 1990s during which the five string theories were discovered to be different limits of a single underlying theory:M-theory .The five consistent superstring theories are:

* Thetype I string has one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special in the sense that it is based on unoriented open andclosed string s, while the rest are based on oriented closed strings.

* Thetype II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-chiral (parity conserving) while the IIB theory is chiral (parity violating).

* Theheterotic string theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensionalgauge group s: the heterotic "E"_{8}×"E"_{8}string and the heterotic SO(32) string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32)Lie group s, string theory singles out a quotient Spin(32)/Z_{2}that is not equivalent to SO(32).)Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop

Feynman diagram s cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via theGreen-Schwarz mechanism .**Integrating general relativity and quantum mechanics**General relativity typically deals with situations involving large mass objects in fairly large regions ofspacetime 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 in which they are combined is in the study ofblack hole s. Having "peak density", or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony in order 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 congruence is that, at sub-Planck (an extremely small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with loops. These loops have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of sub-Planck length dimensional warping, there being no matter that is of sub-Planck length.

**The Five Superstring Interactions**There are five ways open and closed strings can interact. An interaction in superstring theory is a

topology changing event. Since superstring theory has to be alocal theory to obeycausality the topology change must only occur at a single point. If C represents a closed string and O an open string, then the five interactions are, symbollically:**OOO + CCC + OOOO + CO + COO**All open superstring theories also contain closed superstrings since closed superstrings can be seen from the fifth interaction, they are unavoidable. Although all these interactions are possible, in practice the most used superstring model is the closed heterotic E8xE8 superstring which only has closed strings and so only the second interaction (CCC) is needed.

**The Mathematics**The single most important equation in (first quantisized bosonic) string theory is the N-point scattering amplitude. This treats the incoming and outgoing strings as points, which in string theory are

tachyons , with momentum $k\_i$ which connect to a string world surface at the surface points $z\_i$. It is given by the followingfunctional integral which integrates (sums) over all possible embeddings of this 2D surface in 26 dimensions.$A\_N\; =\; int\{Dmu\; int\{D\; [X]\; exp\; left(\; -frac\{1\}\{4pialpha\}\; int\{\; partial\_z\; X\_\{mu\}(z,overline\{z\})\; partial\_\{overline\{z\; X^\{mu\}(z,overline\{z\})\}dz^2\; +\; i\; sum\_\{i=1\}^\{N\}\{k\_\{i\; mu\}\; X^\{mu\}(z\_i,overline\{z\}\_i)\; \}\; ight)$

The functional integral can be done because it is a Gaussian to become:

$A\_N\; =\; int\{Dmu\; prod\_\{0+1\}\{\; |z\_i-z\_j|^\{2alpha\; k\_i.k\_j\}\; \}\; \}\; math>$

This is integrated over the various points $z\_i$. Special care must be taken because two parts of this complex region may represent the same point on the 2D surface and you don't want to integrate over them twice. Also you need to make sure you are not integrating multiple times over different paramaterisations of the surface. When this is taken into account it can be used to calculate the 4-point scattering amplitude (the 3-point amplitude is simply a delta function):

$A\_4\; =\; frac\{\; Gamma\; (-1+frac12(k\_1+k\_2)^2)\; Gamma\; (-1+frac12(k\_2+k\_3)^2)\; \}\; \{\; Gamma\; (-2+frac12((k\_1+k\_2)^2+(k\_2+k\_3)^2))\; \}$

Which is a

beta function . It was this beta function which was apparently found before full string theory was developed. With superstrings the equations contain not only the 10D space-time coordinates X but also the grassman coordinates $heta$. Since there are various ways this can be done this leads to different string theories.When integrating over surfaces such as the torus, we end up with equations in terms of

theta functions and elliptic functions such as theDedekind eta function . This is smooth everywhere, which it has to be to make physical sense, only when raised to the 24th power. This is the origin of needing 26 dimensions of space-time for bosonic string theory. The extra two dimensions arise as degrees of freedom of the string surface.**D-Branes**D-Branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of a

Kaluza-Klein compactification of 11D M-Theory which 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.$partial\_z\; ightarrow\; partial\_z\; +iA\_z(z,overline\{z\})$

In

**type 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.**Why Five Superstring Theories?**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:The heterotic superstrings come in two types SO(32) and E8xE8 as indicated above and the type I superstrings include open strings.

**Beyond Superstring Theory**It is commonly believed that the 5 superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Unfortunately because the action for this involves quartic terms and higher so is not

Gaussian 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 dimensionsM-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 new unknown symmetries of nature are found, such as noncommutative geometry for example. It is thought, however, that 16 is probably the maximum since O(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:$int\_\{-infty\}^\{infty\}\{exp(\{a\; x^4+b\; x^3+c\; x^2+d\; x+f\})dx\}\; =\; e^fsum\_\{n,m,p=0\}^\{infty\}\{\; frac\{\; b^\{4n\{(4n)!\}frac\{c^\{2m\{(2m)!\}frac\{d^\{4p\{(4p)!\}\; frac\{\; Gamma(3n+m+p+frac14)\; \}\{a^\{3n+m+p+frac14\}\; \}\; \}$

In the case of membranes the series would correspond to sums of various membrane interactions that are not seen in string theory.

**Compactification**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 will 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, the "known" symmetries includingsupersymmetry currently restrict thespinors to have 32-components which limits the number of dimensions to 11 (or 12 if you include two time dimensions.) Some commentators (e.g.John Baez et al) have speculated that the exceptionallie groups E_{6}, E_{7}and E_{8}having maximum orthogonal subgroups O(10), O(12) and O(16) may be related to theories in 10, 12 and 16 dimensions; 10 dimensions corresponding tostring theory and the 12 and 16 dimensional theories being yet undiscovered but would be theories bases on 3-branes and 7-branes respectively. However this is a minority view within the string community. Since E_{7}is some sense F_{4}quaternified and E_{8}is F_{4}octonified, then 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 to extend superstring theory beyond the current 10 dimensional theory but so far none have been successful.**Kac-Moody algebras**Since strings can have an infinite number of modes, the symmetry used to describe string theory is based on infinite dimensional Lie algebras. Some Kac-Moody algebras that have been considered as symmetries for

M-Theory have been E_{10}and E_{11}and their supersymmetric extensions.**See also***

AdS/CFT

*Grand unification theory

*List of string theory topics

*M-theory

*Quantum gravity

*String theory

*Large Hadron Collider

*String field theory **References***cite book|last=Kaku|first=Michio|title=Introduction to Superstring and M-Theory|edition=2nd edition|publisher=

Springer-Verlag |location=New York ,USA |year=1999

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**superstring theory**— string theory string the o*ry (str[i^]ng th[=e] [ o]*r[y^]), n. (Physics) A mathematical theory for describing the properties of fundamental particles, which represents the particles as one dimensional string like objects, which exist in the… … The Collaborative International Dictionary of English**superstring theory**— grand unified theory grand unified theory, grand unification theory grand unification theory . (Theoretical physics) Any of a class of physics theories that attempts to explain the electroweak forces, stong force, and gravitation within a single… … The Collaborative International Dictionary of English**superstring theory**— /sooh peuhr string / any supersymmetric string theory in which each type of elementary particle is treated as a vibration of a single fundamental string (superstring) at a particular frequency. * * * Any of a number of theories in particle… … Universalium**superstring theory**— su′per•string theo ry [[t]ˈsu pərˌstrɪŋ[/t]] n. phs any supersymmetric string theory in which each type of elementary particle is treated as a vibration of a single fundamental string(superstring)at a particular frequency … From formal English to slang**superstring theory**— /sooh peuhr string / any supersymmetric string theory in which each type of elementary particle is treated as a vibration of a single fundamental string (superstring) at a particular frequency … Useful english dictionary**superstring theory**— /ˈsupəstrɪŋ θɪəri/ (say soohpuhstring thearree) noun a combination of string theory with the concept of supersymmetry, which is able to incorporate gravitation with the three other fundamental forces … Australian English dictionary**Superstring**— Als Superstringtheorie (abkürzend meist Stringtheorie) bezeichnet man eine Sammlung eng verwandter hypothetischer physikalischer Modelle, die alle bisher beobachteten Fundamentalkräfte der Physik einheitlich erklären. Sie gilt damit als Ansatz… … Deutsch Wikipedia**Superstring-Theorie**— Als Superstringtheorie (abkürzend meist Stringtheorie) bezeichnet man eine Sammlung eng verwandter hypothetischer physikalischer Modelle, die alle bisher beobachteten Fundamentalkräfte der Physik einheitlich erklären. Sie gilt damit als Ansatz… … Deutsch Wikipedia**Theory of everything**— A theory of everything (TOE) is a putative theory of theoretical physics that fully explains and links together all known physical phenomena. Initially, the term was used with an ironic connotation to refer to various overgeneralized theories.… … Wikipedia**theory**— /thee euh ree, thear ee/, n., pl. theories. 1. a coherent group of general propositions used as principles of explanation for a class of phenomena: Einstein s theory of relativity. 2. a proposed explanation whose status is still conjectural, in… … Universalium