HOME

TheInfoList



OR:

Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of
string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
that accounts for both fermions and
bosons In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...
and incorporates
supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
to model gravity. Since the
second superstring revolution The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum ...
, the five superstring theories are regarded as different limits of a single theory tentatively called
M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witt ...
.


Background

The deepest problem in
theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
is harmonizing the theory of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, which describes gravitation and applies to large-scale structures (
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s,
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System ...
, super clusters), with
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, which describes the other three
fundamental forces In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
acting on the atomic scale. The development of a
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
of a force invariably results in infinite possibilities. Physicists developed the technique of renormalization to eliminate these infinities; this technique works for three of the four fundamental forces— electromagnetic, strong nuclear and weak nuclear forces—but not for
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
. Development of quantum theory of gravity therefore requires different means than those used for the other forces. According to the theory, the fundamental constituents of reality are strings of the Planck length (about 10−33 cm) that vibrate at resonant frequencies. Every string, in theory, has a unique resonance, or harmonic. Different harmonics determine different fundamental particles. The tension in a string is on the order of the Planck force (1044
newtons The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in r ...
). The
graviton In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathem ...
(the proposed
messenger particle In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical fi ...
of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero.


History

Investigating how a string theory may include fermions in its spectrum led to the invention of
supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
(in the West) in 1971, 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 to
quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
,
particle In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from ...
and
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...
,
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
, and
pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...
.


Lack of experimental evidence

Superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and recent research at the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundr ...
(LHC) and
Tevatron The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collider ...
has excluded some of the ranges. For instance, the mass constraint of the Minimal Supersymmetric Standard Model
squarks In supersymmetric extension to the Standard Model (SM) of physics, a sfermion is a hypothetical spin-0 superpartner particle (sparticle) of its associated fermion. Each particle has a superpartner with spin that differs by . Fermions in the SM h ...
has been up to 1.1 TeV, and gluinos up to 500 GeV. No report on suggesting large extra dimensions has been delivered from LHC. There have been no principles so far to limit the number of vacua in the concept of a landscape of vacua. Some particle physicists became disappointed by the lack of experimental verification of supersymmetry, and some have already discarded it;
Jon Butterworth Jonathan Mark Butterworth is a Professor of Physics at University College London (UCL) working on the ATLAS experiment at CERN's Large Hadron Collider (LHC). His popular science book ''Smashing Physics'', (available as “Most Wanted Particle� ...
at
University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = ...
said that we had no sign of supersymmetry, even in higher energy region, excluding the superpartners 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 at CERN in the foreseeable future.


Extra dimensions

Our physical space is observed to have three large spatial
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
s and, along with
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
, is a boundless 4-dimensional continuum known as
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
. However, nothing prevents a theory from including more than 4 dimensions. In the case of
string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
,
consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
requires
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
to have 10 dimensions (3D regular space + 1 time + 6D hyperspace). The fact that we see only 3 dimensions of space can be explained by one of two mechanisms: either the extra dimensions are compactified on a very small scale, or else our world may live on a 3-dimensional
submanifold In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which ...
corresponding to a brane, on which all known particles besides gravity would be restricted. If the extra dimensions are compactified, then the extra 6 dimensions must be in the form of a
Calabi–Yau manifold In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstrin ...
. Within the more complete framework of M-theory, they would have to take form of a
G2 manifold In differential geometry, a ''G''2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in ''G''2. The group G_2 is one of the five exceptional simple Lie groups. It can be described as the automorphism group of th ...
. A particular exact symmetry of string/M-theory called
T-duality In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories descr ...
(which exchanges momentum modes for
winding number In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point, i.e., the curve's number of t ...
and sends compact dimensions of radius R to radius 1/R), has led to the discovery of equivalences between different Calabi–Yau manifolds called mirror symmetry. Superstring theory is not the first theory to propose extra spatial dimensions. It can be seen as building upon the Kaluza–Klein theory, which proposed a 4+1 dimensional (5D) theory of gravity. When compactified on a circle, the gravity in the extra dimension precisely describes
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
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 of
parity violation In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point ref ...
, 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.


Number of superstring theories

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 the
second superstring revolution The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum ...
in the 1990s, which suggests that the five string theories might be different limits of a single underlying theory, called M-theory. This remains a
conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in ...
. The five consistent superstring theories are: * The
type I string In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and the only one which contains ...
has one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special in the sense that it is based on unoriented
open Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * Open (Blues Image album), ''Open'' (Blues Image album), 1969 * Open (Gotthard album), ''Open'' (Gotthard album), 1999 * Open (C ...
and
closed string In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often h ...
s, while the rest are based on oriented closed strings. * The type 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). * The
heterotic string In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbrevi ...
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-dimensional gauge groups: 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 In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addi ...
s, string theory singles out a quotient Spin(32)/Z2 that is not equivalent to SO(32).) Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop
Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
s cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the Green–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 the
mathematical structure In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additiona ...
called composition algebra. In the findings of
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...
there are just seven composition algebras over the field of
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
s. 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".


Integrating general relativity and quantum mechanics

General relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
typically deals with situations involving large mass objects in fairly large regions of
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
whereas
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
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 of
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
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 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 Planck 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 the Planck 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 Crunch The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentia ...
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 one string, at which point it would actually begin expanding.


Mathematics


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 that contains membranes. Because compactification of a geometric theory produces extra vector fields the D-branes can be included in the action by adding an extra U(1) vector field to the string action. : \partial_z \rightarrow \partial_z +iA_z(z,\overline) 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. 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.


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 In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sli ...
. 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 E8×E8 as indicated above and the type I superstrings include open strings.


Beyond superstring theory

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 not
Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponym ...
, 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 the
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
. 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 \exp() \, dx = e^f \sum_^\infty \frac \frac \frac \frac 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 In string theory, D-branes, short for ''Dirichlet membrane'', are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Jin Dai, Leigh, and Polc ...
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, the ''known'' symmetries including
supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
currently restrict the
spinors In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a sli ...
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 John Carlos Baez (; born June 12, 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He has worked on spin foams in loop quantum gravity, appli ...
et al.) have speculated that the exceptional Lie 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 the noncommutative geometry based on the
quaternions In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quater ...
and octonions 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.


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 E10 and E11 and their supersymmetric extensions.


See also

*
AdS/CFT correspondence In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter ...
* dS/CFT correspondence *
Grand unification theory A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although th ...
*
List of string theory topics This is a list of string theory topics. String theory * Strings * Nambu–Goto action * Polyakov action * Bosonic string theory * Superstring theory ** Type I string ** Type II string *** Type IIA string theory *** Type IIB string theo ...
*
String field theory String or strings may refer to: * String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian ani ...


References


Cited sources

* * {{DEFAULTSORT:Superstring Theory String theory Supersymmetry Supersymmetric quantum field theory Physics beyond the Standard Model