History of string theory
Encyclopedia
The history of string theory is probably more relevant to its core science than histories of other physical sciences. String theory
is presently, and essentially, a non physically testable science, and thus arguably not Physics
, yet its derivation parallels testable physics. Consequently an understanding of the theory's development has useful relevance within its ascribed discipline.
in 1943, picked up and advocated by many prominent theorists starting in the late 1950s and throughout the 1960s, which was discarded and marginalized in the 1970s to disappear by the 1980s. It was forgotten because a few of the ideas were deeply mistaken, because some of its mathematical methods were alien, and because quantum chromodynamics
supplanted it as an approach to the strong interactions.
The program was called the S-matrix theory
, and it was a radical rethinking of the foundation of physical law. By the 1940s it was clear that the proton
and the neutron
were not pointlike particles like the electron. Their magnetic moment
was very different from that of a pointlike spin-1/2 charged particle, and by too much to attribute the difference to a small perturbation. Their interactions were so strong that they scattered like a small sphere, not like a point. Heisenberg proposed that the strongly interacting particles were in fact extended objects, and because there are difficulties of principle with extended relativistic particles, he proposed that the notion of a space-time point broke down at nuclear scales.
Without space and time, it is difficult to formulate a physical theory. Heisenberg believed that the solution to this problem is to focus on the observable quantities—those things measurable by experiments. An experiment only sees a microscopic quantity if it can be transferred by a series of events to the classical devices that surround the experimental chamber. The objects that fly to infinity are stable particles, in quantum superpositions of different momentum states.
Heisenberg proposed that even when space and time are unreliable, the notion of momentum state, which is defined far away from the experimental chamber, still works. The physical quantity he proposed as fundamental is the quantum mechanical amplitude for a group of incoming particles to turn into a group of outgoing particles, and he did not admit that there were any steps in between.
The S-matrix is the quantity that describes how a superposition of incoming particles turn into outgoing ones. Heisenberg proposed to study the S-matrix directly, without any assumptions about space-time structure. But when transitions from the far-past to the far-future occur in one step with no intermediate steps, it is difficult to calculate anything. In quantum field theory
, the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles. In this proposed S-matrix theory, there are no local quantities at all.
Heisenberg proposed to use unitarity to determine the S-matrix. In all conceivable situations, the sum of the squares of the amplitudes must be equal to 1. This property can determine the amplitude in a quantum field theory order by order in a perturbation series once the basic interactions are given, and in many quantum field theories the amplitudes grow too fast at high energies to make a unitary S-matrix. But without extra assumptions on the high-energy behavior unitarity is not enough to determine the scattering, and the proposal was ignored for many years.
Heisenberg's proposal was reinvigorated in the late 1950s when several theorists recognized that dispersion relations like those discovered by Hendrik Kramers and Ralph Kronig
allow a notion of causality to be formulated, a notion that events in the future would not influence events in the past, even when the microscopic notion of past and future are not clearly defined. The dispersion relations were analytic
properties of the S-matrix, and they were more stringent conditions than those that follow from unitarity alone.
Prominent advocates of this approach were Stanley Mandelstam
and Geoffrey Chew
. Mandelstam had discovered the double-dispersion relations, a new and powerful analytic form, in 1958, and believed that it would be the key to progress in the intractable strong interactions.
, the neutron
and the Lambda (see Sakata model), Chew believed that none of these particles are fundamental. Sakata's approach was reworked in the 1960s into the quark
model by Murray Gell-Mann
and George Zweig
by making the charges of the hypothetical constituents fractional and rejecting the idea that they were observed particles. Chew's approach was then considered more mainstream because it did not introduce fractional charges and because it only focused on the experimentally measurable S-matrix elements, not on hypothetical pointlike constituents.
In 1958 Tullio Regge
, a young theorist in Italy discovered that bound states in quantum mechanics can be organized into families with different angular momentum called Regge trajectories. This idea was generalized to relativistic quantum mechanics by Mandelstam, Vladimir Gribov
and Marcel Froissart, using a mathematical method discovered decades earlier by Arnold Sommerfeld
and Kenneth Marshall Watson.
Geoffrey Chew
and Steven Frautschi
recognized that the meson
s made Regge trajectories in straight lines, which implied, via Regge theory, that the scattering of these particles would have very strange behavior—it should fall off exponentially quickly at large angles. With this realization, theorists hoped to construct a theory of composite particles on Regge trajectories, whose scattering amplitudes had the asymptotic form demanded by Regge theory. Since the interactions fall off fast at large angles, the scattering theory would have to be somewhat holistic: Scattering off a pointlike constituent leads to large angular deviations at high energies.
, was constructed by Gabriele Veneziano
in 1968, who noted that the Euler
Beta function could be used to describe 4-particle scattering amplitude data for particles on Regge trajectories. The Veneziano scattering amplitude was quickly generalized to an N-particle amplitude by Ziro Koba and Holger Bech Nielsen
, and to what are now recognized as closed strings by Miguel Virasoro
and Joel A. Shapiro. Dual resonance models for strong interactions were a popular subject of study 1968-1974.
, Holger Bech Nielsen
, and Leonard Susskind
presented a physical interpretation of Euler's formula by representing nuclear forces as vibrating, one-dimensional strings. However, this string-based description of the strong force made many predictions that directly contradicted experimental findings. The scientific community lost interest in string theory as a theory of strong interactions in 1974 when quantum chromodynamics
became the main focus of theoretical research.
In 1974 John H. Schwarz and Joel Scherk
, and independently Tamiaki Yoneya
, studied the boson
-like patterns of string vibration and found that their properties exactly matched those of the graviton
, the gravitational force's hypothetical "messenger" particle. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development of bosonic string theory
, which is still the version first taught to many students.
String theory is formulated in terms of the Polyakov action
, which describes how strings move through space and time. Like springs, the strings want to contract to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics
to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates — in essence, by the "note" the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.
Early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety.
The earliest string model, which incorporated only bosons, has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon
that obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermion
s in its spectrum led to the invention of supersymmetry
, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories
; several different kinds have been described.
s as well as the interactions between them. Hundreds of physicists started to work on string theory
as the most promising idea to unify physical theories. The revolution was started by a discovery of anomaly cancellation
in type I string theory
via the Green-Schwarz mechanism
in 1984. Several other ground-breaking discoveries, such as the heterotic string
, were made in 1985. It was also realised in 1985 that to obtain
supersymmetry
, the six small extra dimensions need to be compactified
on a Calabi-Yau manifold
.
Discover
magazine in the November 1986 issue (vol 7, #11) featured a cover story written by Gary Taubes
"Everything's Now Tied to Strings" which explained string theory for a popular audience.
and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory
. These discoveries sparked the second superstring revolution that took place approximately between 1994 and 1997.
The different versions of superstring theory
were unified, as long hoped, by new equivalences. These are known as S-duality
, T-duality
, U-duality
, mirror symmetry
, and conifold
transitions. The different theories of strings were also connected to a new 11-dimensional theory called M-theory
.
In the mid 1990s, Joseph Polchinski
discovered that the theory requires the inclusion of higher-dimensional objects, called D-brane
s. These added an additional rich mathematical structure to the theory, and opened many possibilities for constructing realistic cosmological models in the theory. Their analysis - especially the analysis of a special type of branes called D-branes - led to the AdS/CFT correspondence, the microscopic understanding of the thermodynamic properties of black holes, and many other developments.
In 1997 Juan Maldacena conjectured a relationship between string theory and a gauge theory
called N=4 supersymmetric Yang-Mills theory. This conjecture, called the AdS/CFT correspondence
has generated a great deal of interest in the field and is now well accepted. It is a concrete realization of the holographic principle
, which has far-reaching implications for black hole
s, locality
and information
in physics, as well as the nature of the gravitational interaction.
, which suggests that string theory has a large number of inequivalent vacua, led to much discussion of what string theory might eventually be expected to predict, and how cosmology
can be incorporated into the theory.
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
is presently, and essentially, a non physically testable science, and thus arguably not Physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, yet its derivation parallels testable physics. Consequently an understanding of the theory's development has useful relevance within its ascribed discipline.
1943-1958: S-Matrix
String theory is an outgrowth of a research program begun by Werner HeisenbergWerner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
in 1943, picked up and advocated by many prominent theorists starting in the late 1950s and throughout the 1960s, which was discarded and marginalized in the 1970s to disappear by the 1980s. It was forgotten because a few of the ideas were deeply mistaken, because some of its mathematical methods were alien, and because quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
supplanted it as an approach to the strong interactions.
The program was called the S-matrix theory
S-matrix theory
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics.It avoided the notion of space and time by replacing it with abstract mathematical properties of the S-matrix...
, and it was a radical rethinking of the foundation of physical law. By the 1940s it was clear that the proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
and the neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
were not pointlike particles like the electron. Their magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
was very different from that of a pointlike spin-1/2 charged particle, and by too much to attribute the difference to a small perturbation. Their interactions were so strong that they scattered like a small sphere, not like a point. Heisenberg proposed that the strongly interacting particles were in fact extended objects, and because there are difficulties of principle with extended relativistic particles, he proposed that the notion of a space-time point broke down at nuclear scales.
Without space and time, it is difficult to formulate a physical theory. Heisenberg believed that the solution to this problem is to focus on the observable quantities—those things measurable by experiments. An experiment only sees a microscopic quantity if it can be transferred by a series of events to the classical devices that surround the experimental chamber. The objects that fly to infinity are stable particles, in quantum superpositions of different momentum states.
Heisenberg proposed that even when space and time are unreliable, the notion of momentum state, which is defined far away from the experimental chamber, still works. The physical quantity he proposed as fundamental is the quantum mechanical amplitude for a group of incoming particles to turn into a group of outgoing particles, and he did not admit that there were any steps in between.
The S-matrix is the quantity that describes how a superposition of incoming particles turn into outgoing ones. Heisenberg proposed to study the S-matrix directly, without any assumptions about space-time structure. But when transitions from the far-past to the far-future occur in one step with no intermediate steps, it is difficult to calculate anything. In quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles. In this proposed S-matrix theory, there are no local quantities at all.
Heisenberg proposed to use unitarity to determine the S-matrix. In all conceivable situations, the sum of the squares of the amplitudes must be equal to 1. This property can determine the amplitude in a quantum field theory order by order in a perturbation series once the basic interactions are given, and in many quantum field theories the amplitudes grow too fast at high energies to make a unitary S-matrix. But without extra assumptions on the high-energy behavior unitarity is not enough to determine the scattering, and the proposal was ignored for many years.
Heisenberg's proposal was reinvigorated in the late 1950s when several theorists recognized that dispersion relations like those discovered by Hendrik Kramers and Ralph Kronig
Ralph Kronig
Ralph Kronig was a German-American physicist . He is noted for the discovery of particle spin and for his theory of x-ray absorption spectroscopy...
allow a notion of causality to be formulated, a notion that events in the future would not influence events in the past, even when the microscopic notion of past and future are not clearly defined. The dispersion relations were analytic
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
properties of the S-matrix, and they were more stringent conditions than those that follow from unitarity alone.
Prominent advocates of this approach were Stanley Mandelstam
Stanley Mandelstam
Stanley Mandelstam is a South African-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations...
and Geoffrey Chew
Geoffrey Chew
Geoffrey F. Chew is an American theoretical physicist.He has worked as a professor of physics at the UC Berkeley since 1957 and has been an emeritus since 1991. Chew holds a PhD in theoretical particle physics from the University of Chicago. Between 1950 and 1956, he was a physics faculty member...
. Mandelstam had discovered the double-dispersion relations, a new and powerful analytic form, in 1958, and believed that it would be the key to progress in the intractable strong interactions.
1958-1968: Regge theory and bootstrap models
At this time, many strongly interacting particles of ever higher spins were discovered, and it became clear that they were not all fundamental. While Japanese physicist Sakata proposed that the particles could be understood as bound states of just three of them--- the protonProton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
, the neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
and the Lambda (see Sakata model), Chew believed that none of these particles are fundamental. Sakata's approach was reworked in the 1960s into the quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
model by Murray Gell-Mann
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...
and George Zweig
George Zweig
George Zweig was originally trained as a particle physicist under Richard Feynman and later turned his attention to neurobiology...
by making the charges of the hypothetical constituents fractional and rejecting the idea that they were observed particles. Chew's approach was then considered more mainstream because it did not introduce fractional charges and because it only focused on the experimentally measurable S-matrix elements, not on hypothetical pointlike constituents.
In 1958 Tullio Regge
Tullio Regge
Tullio Regge is an Italian theoretical physicist. He obtained a degree in physics from the University of Turin in 1952, and a Ph.D. in physics from the University of Rochester in 1957 under the direction of Robert Marshak. From 1958 to 1959 Regge held a post at the Max Planck Institute for...
, a young theorist in Italy discovered that bound states in quantum mechanics can be organized into families with different angular momentum called Regge trajectories. This idea was generalized to relativistic quantum mechanics by Mandelstam, Vladimir Gribov
Vladimir Gribov
Vladimir Naumovich Gribov was a prominent Russian theoretical physicist, who worked on high-energy physics, quantum field theory and the Regge theory of the strong interactions.His best known contributions are the pomeron, the DGLAP equations, and the Gribov copies.-Life:Gribov completed his...
and Marcel Froissart, using a mathematical method discovered decades earlier by Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
and Kenneth Marshall Watson.
Geoffrey Chew
Geoffrey Chew
Geoffrey F. Chew is an American theoretical physicist.He has worked as a professor of physics at the UC Berkeley since 1957 and has been an emeritus since 1991. Chew holds a PhD in theoretical particle physics from the University of Chicago. Between 1950 and 1956, he was a physics faculty member...
and Steven Frautschi
Steven Frautschi
Steven Frautschi is an American theoretical physicist, Professor of Physics at the California Institute of Technology. He is known for his contributions to the bootstrap theory of the strong interactions....
recognized that the meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s made Regge trajectories in straight lines, which implied, via Regge theory, that the scattering of these particles would have very strange behavior—it should fall off exponentially quickly at large angles. With this realization, theorists hoped to construct a theory of composite particles on Regge trajectories, whose scattering amplitudes had the asymptotic form demanded by Regge theory. Since the interactions fall off fast at large angles, the scattering theory would have to be somewhat holistic: Scattering off a pointlike constituent leads to large angular deviations at high energies.
1968-1974: Dual resonance model
The first theory of this sort, the dual resonance modelDual resonance model
In theoretical physics, a dual resonance model arose the early investigation of string theory as an S-matrix theory of the strong interaction....
, was constructed by Gabriele Veneziano
Gabriele Veneziano
Gabriele Veneziano, born in Florence, Italy), is an Italian theoretical physicist and the founder of string theory. . Has spent most of his scientific activities at CERN in Geneva, Switzerland...
in 1968, who noted that the Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
Beta function could be used to describe 4-particle scattering amplitude data for particles on Regge trajectories. The Veneziano scattering amplitude was quickly generalized to an N-particle amplitude by Ziro Koba and Holger Bech Nielsen
Holger Bech Nielsen
Holger Bech Nielsen is a Danish theoretical physicist, professor at the Niels Bohr Institute, at the University of Copenhagen, where he started studying physics in 1961....
, and to what are now recognized as closed strings by Miguel Virasoro
Miguel Angel Virasoro
Miguel Angel Virasoro is an Argentine physicist who did most of his work in Italy. The Virasoro algebra is named after him. Together with Giorgio Parisi and Marc Mezard he discovered the...
and Joel A. Shapiro. Dual resonance models for strong interactions were a popular subject of study 1968-1974.
1974-1984: Superstring theory
In 1970, Yoichiro NambuYoichiro Nambu
is a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded a one-half share of the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in...
, Holger Bech Nielsen
Holger Bech Nielsen
Holger Bech Nielsen is a Danish theoretical physicist, professor at the Niels Bohr Institute, at the University of Copenhagen, where he started studying physics in 1961....
, and Leonard Susskind
Leonard Susskind
Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology...
presented a physical interpretation of Euler's formula by representing nuclear forces as vibrating, one-dimensional strings. However, this string-based description of the strong force made many predictions that directly contradicted experimental findings. The scientific community lost interest in string theory as a theory of strong interactions in 1974 when quantum chromodynamics
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
became the main focus of theoretical research.
In 1974 John H. Schwarz and Joel Scherk
Joël Scherk
Joël Scherk was a French theoretical physicist who studied string theory and supergravity. Together with John H. Schwarz, he figured out that string theory was a theory of quantum gravity in 1974...
, and independently Tamiaki Yoneya
Tamiaki Yoneya
is a physicist. Independently of Joel Scherk and John H. Schwarz, he realized that string theory describes, among other things, the force of gravity. Yoneya has worked on the stringy extension of the uncertainty principle for many years.- References :...
, studied the boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
-like patterns of string vibration and found that their properties exactly matched those of the graviton
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
, the gravitational force's hypothetical "messenger" particle. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development of bosonic string theory
Bosonic string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s.In the early 1970s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory became the real focus...
, which is still the version first taught to many students.
String theory is formulated in terms of the Polyakov action
Polyakov action
In physics, the Polyakov action is the two-dimensional action of a conformal field theory describing the worldsheet of a string in string theory...
, which describes how strings move through space and time. Like springs, the strings want to contract to minimize their potential energy, but conservation of energy prevents them from disappearing, and instead they oscillate. By applying the ideas of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle. The mass of each particle, and the fashion with which it can interact, are determined by the way the string vibrates — in essence, by the "note" the string sounds. The scale of notes, each corresponding to a different kind of particle, is termed the "spectrum" of the theory.
Early models included both open strings, which have two distinct endpoints, and closed strings, where the endpoints are joined to make a complete loop. The two types of string behave in slightly different ways, yielding two spectra. Not all modern string theories use both types; some incorporate only the closed variety.
The earliest string model, which incorporated only bosons, has problems. Most importantly, the theory has a fundamental instability, believed to result in the decay of space-time itself. Additionally, as the name implies, the spectrum of particles contains only bosons, particles like the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
that obey particular rules of behavior. While bosons are a critical ingredient of the Universe, they are not its only constituents. Investigating how a string theory may include fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s in its spectrum led to the invention of supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
; several different kinds have been described.
1984-1989: first superstring revolution
The first superstring revolution is a period of important discoveries roughly between 1984 and 1986. It was realised that string theory was capable of describing all elementary particleElementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s as well as the interactions between them. Hundreds of physicists started to work on string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
as the most promising idea to unify physical theories. The revolution was started by a discovery of anomaly cancellation
Anomaly (physics)
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
in type I string theory
Type I string theory
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 and which contains not only closed strings, but also open strings.The classic 1976 work of Ferdinando Gliozzi, Joel Scherk and...
via the Green-Schwarz mechanism
Green-Schwarz mechanism
The Green–Schwarz mechanism is the main discovery that started the first superstring revolution in superstring theory.-Discovery:In 1984, Michael Green and John H...
in 1984. Several other ground-breaking discoveries, such as the heterotic string
Heterotic string
In physics, a heterotic string is a peculiar mixture of the bosonic string and the superstring...
, were made in 1985. It was also realised in 1985 that to obtain
supersymmetrySupersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
, the six small extra dimensions need to be compactified
Compactification (physics)
In physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic....
on a Calabi-Yau manifold
Calabi-Yau manifold
A Calabi-Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics...
.
Discover
Discover (magazine)
Discover is an American science magazine that publishes articles about science for a general audience. The monthly magazine was launched in October 1980 by Time Inc. It was sold to Family Media, the owners of Health, in 1987. Walt Disney Company bought the magazine when Family Media went out of...
magazine in the November 1986 issue (vol 7, #11) featured a cover story written by Gary Taubes
Gary Taubes
Gary Taubes is an American science writer.He is the author of Nobel Dreams , Bad Science: The Short Life and Weird Times of Cold Fusion , and Good Calories, Bad Calories , titled The Diet Delusion in the UK and Australia. His book Why We Get Fat: And What to Do About It was released in December...
"Everything's Now Tied to Strings" which explained string theory for a popular audience.
1994-2000: second superstring revolution
In the early 1990s, Edward WittenEdward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
and others found strong evidence that the different superstring theories were different limits of a new 11-dimensional theory called M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
. These discoveries sparked the second superstring revolution that took place approximately between 1994 and 1997.
The different versions of superstring theory
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
were unified, as long hoped, by new equivalences. These are known as S-duality
S-duality
In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
, T-duality
T-duality
T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
, U-duality
U-duality
In physics, U-duality is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the "U-duality group" of M-theory as defined on a particular background space . This is the union of all the S- and T-dualities...
, mirror symmetry
Mirror symmetry
In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden...
, and conifold
Conifold
In mathematics and string theory, a conifold is a generalization of a manifold. Unlike manifolds, conifolds can contain conical singularities i.e. points whose neighbourhoods look like cones over a certain base...
transitions. The different theories of strings were also connected to a new 11-dimensional theory called M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
.
In the mid 1990s, Joseph Polchinski
Joseph Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...
discovered that the theory requires the inclusion of higher-dimensional objects, called D-brane
D-brane
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. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989...
s. These added an additional rich mathematical structure to the theory, and opened many possibilities for constructing realistic cosmological models in the theory. Their analysis - especially the analysis of a special type of branes called D-branes - led to the AdS/CFT correspondence, the microscopic understanding of the thermodynamic properties of black holes, and many other developments.
In 1997 Juan Maldacena conjectured a relationship between string theory and a gauge theory
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
called N=4 supersymmetric Yang-Mills theory. This conjecture, called the AdS/CFT correspondence
AdS/CFT correspondence
In physics, the AdS/CFT correspondence , sometimes called the Maldacena duality, is the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more...
has generated a great deal of interest in the field and is now well accepted. It is a concrete realization of the holographic principle
Holographic principle
The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...
, which has far-reaching implications for black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s, locality
Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...
and information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
in physics, as well as the nature of the gravitational interaction.
2000s
In the 2000s, the discovery of the string theory landscapeString theory landscape
The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory. The "landscape" includes so many possible configurations that some physicists think that the known laws of physics, the standard model and general relativity with a positive...
, which suggests that string theory has a large number of inequivalent vacua, led to much discussion of what string theory might eventually be expected to predict, and how cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
can be incorporated into the theory.