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{{string theory}}
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 gravity]], [[particle physics|particle]] and [[condensed matter physics]], [[cosmology]], and [[pure mathematics]].

== 1943–1959: S-matrix theory ==
String theory represents an outgrowth of [[S-matrix theory]],<ref>Rickles 2014, p. 28 n. 17: "S-matrix theory had enough time to spawn string theory".</ref> a research program begun by [[Werner Heisenberg]] in 1943<ref>{{cite journal | last1 = Heisenberg | first1 = W. | year = 1943 | title = Die "beobachtbaren Größen" in der Theorie der Elementarteilchen | journal = Zeitschrift für Physik | volume = 120 | issue = 7| pages = 513–538 | doi=10.1007/bf01329800| bibcode = 1943ZPhy..120..513H| s2cid = 120706757 }}</ref> following [[John Archibald Wheeler]]'s 1937 introduction of the S-matrix.<ref>{{cite journal | last1 = Wheeler | first1 = John Archibald | year = 1937 | title = On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure | journal = Phys. Rev. | volume = 52 | issue = 11| pages = 1107–1122 | doi=10.1103/physrev.52.1107| bibcode = 1937PhRv...52.1107W| s2cid = 55071722 }}</ref> Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. The field became marginalized and discarded in the mid-1970s<ref>Rickles 2014, p. 113: "An unfortunate (for string theory) series of events terminated the growing popularity that string theory was enjoying in the early 1970s."</ref> and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and because [[quantum chromodynamics]] supplanted it as an experimentally better-qualified approach to the [[strong interactions]].<ref>Rickles 2014, p. 4.</ref>

The theory presented a radical rethinking of the foundations of physical laws. By the 1940s it had become clear that the [[proton]] and the [[neutron]] were not pointlike particles like the electron. Their [[magnetic moment]] differed greatly from that of a pointlike [[spin-½]] charged particle, too much to attribute the difference to a small [[Perturbation theory|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 becomes difficult to formulate a physical theory. Heisenberg proposed a solution to this problem: focusing on the observable quantities&mdash;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]] [[Probability amplitude|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 collection 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 becomes 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 (physics)|unitarity]] to determine the S-matrix. In all conceivable situations, the sum of the squares of the amplitudes must equal 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 revived in 1956 when [[Murray Gell-Mann]] recognized that [[dispersion relations]]—like those discovered by [[Hendrik Kramers]] and [[Ralph Kronig]] in the 1920s (see [[Kramers–Kronig relations]])—allow the formulation of a notion of causality, 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. He also recognized that these relations might be useful in computing observables for the case of strong interaction physics.<ref>Gell-Mann, M. G. (1956). "Dispersion relations in pion-pion and photon-nucleon scattering." In J. Ballam, ''et al.'' (eds.), ''High energy nuclear physics'', in: ''Proceedings of the Sixth Annual Rochester Conference Rochester: New York, USA, April 3–7, 1956'' (pp. 30–6). New York: Interscience Publishers.</ref> The dispersion relations were [[Analytic continuation|analytic]] properties of the S-matrix,<ref name=Rickles29>Rickles 2014, p. 29.</ref> and they imposed more stringent conditions than those that follow from unitarity alone. This development in S-matrix theory stemmed from Murray Gell-Mann and [[Marvin Leonard Goldberger]]'s (1954) discovery of [[Crossing (physics)|crossing symmetry]], another condition that the S-matrix had to fulfil.<ref>Gell-Mann, M., and Goldberger, M. L. (1954). "The scattering of low energy photons by particles of spin 1/2." ''Physical Review'', '''96''', 1433–8.</ref><ref name=Rickles29/>

Prominent advocates of the new "dispersion relations" approach included [[Stanley Mandelstam]]<ref name=Mandelstam58/> and [[Geoffrey Chew]],<ref>{{cite journal | last1 = Chew | first1 = G. F. | last2 = Goldberger | first2 = M. L. | last3 = Low | first3 = F. E. | author-link3 = Francis E. Low | last4 = Nambu | first4 = Y. | year = 1957 | title = Application of dispersion relations to low energy meson-nucleon scattering | url = https://authors.library.caltech.edu/12453/1/CHEpr57b.pdf| journal = Physical Review | volume = 106 | issue = 6 | pages = 1337–1344 | doi= 10.1103/physrev.106.1337| bibcode = 1957PhRv..106.1337C | s2cid = 121551470 }}</ref> both at [[UC Berkeley]] at the time. Mandelstam discovered the [[double dispersion relation]]s, a new and powerful analytic form, in 1958,<ref name=Mandelstam58>{{cite journal
 | last1 = Mandelstam | first1 = S. | year = 1958
 | title = Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity general theory
 | journal = Physical Review | volume = 112
 | issue = 4| pages = 1344–1360
 | doi= 10.1103/physrev.112.1344
 | bibcode = 1958PhRv..112.1344M
}}
</ref> and believed that it would provide the key to progress in the intractable strong interactions.

== 1959–1968: Regge theory and bootstrap models ==
{{main|Regge theory}}

By the late 1950s, many strongly interacting particles of ever higher spins had been discovered, and it became clear that they were not all fundamental. While Japanese physicist [[Shoichi Sakata]] proposed that the particles could be understood as [[bound state]]s of just three of them (the proton, the neutron and the [[Lambda baryon|Lambda]]; see [[Sakata model]]),<ref>{{cite journal |last=Sakata |first=S. |year=1956 |title=On a composite model for the new particles |journal=Progress of Theoretical Physics |volume=16 |issue=6 |page=686&ndash;688 |bibcode=1956PThPh..16..686S |doi=10.1143/PTP.16.686 |doi-access=free}}</ref> Geoffrey Chew believed that none of these particles are fundamental<ref>Chew, G. (1962). ''S-Matrix theory of strong interactions.'' New York: W.A. Benjamin, p. 32.</ref><ref>{{cite journal | last1 = Kaiser | first1 = D | year = 2002 | title = Nuclear democracy: Political engagement, pedagogical reform, and particle physics in postwar America | journal = Isis | volume = 93 | issue = 2| pages = 229–268 | doi=10.1086/344960| pmid = 12198794 | s2cid = 28620266 }}</ref> (for details, see [[Bootstrap model]]). Sakata's approach was reworked in the 1960s into the [[quark model]] by [[Murray Gell-Mann]] and [[George Zweig]] by making the [[Electric charge|charges]] of the hypothetical constituents [[Fraction (mathematics)|fractional]] and rejecting the idea that they were observed particles. At the time, Chew's approach was considered more mainstream because it did not introduce fractional charge values and because it focused on experimentally measurable S-matrix elements, not on hypothetical pointlike constituents.

[[File:Chew-Frautschi plot.svg|thumb|Chew-Frautschi plot showing the angular momentum J as a function of the square mass of some particles. An example of Regge trajectories.]]

In 1959, [[Tullio Regge]], a young theorist in Italy, discovered that bound states in quantum mechanics can be organized into families known as [[Regge trajectories]], each family having distinctive [[angular momentum|angular momenta]].<ref>Regge, Tullio, "Introduction to complex angular momentum," ''Il Nuovo Cimento Series'' 10, Vol. 14, 1959, p. 951.</ref> This idea was generalized to [[relativistic quantum mechanics]] by [[Stanley Mandelstam]], [[Vladimir Gribov]] and [[Marcel Froissart]], using a mathematical method (the [[Sommerfeld–Watson representation]]) discovered decades earlier by [[Arnold Sommerfeld]] and [[Kenneth M. Watson]]: the result was dubbed the [[Froissart–Gribov formula]].<ref name="S-Matrix Past and Future">{{cite arXiv |last=White |first=Alan R. |date=2000-02-29 |title=The Past and Future of S-Matrix Theory |eprint=hep-ph/0002303}}</ref>

In 1961, Geoffrey Chew and [[Steven Frautschi]] recognized that [[meson]]s had straight line Regge trajectories<ref>{{cite journal|doi = 10.1103/PhysRevLett.7.394|last1 = Chew|journal = Physical Review Letters|first1 = Geoffrey|last2 = Frautschi|first2 = S.|title = Principle of Equivalence for all Strongly Interacting Particles within the S-Matrix Framework|volume = 7|year = 1961|pages = 394–397|bibcode = 1961PhRvL...7..394C|issue = 10|url = https://authors.library.caltech.edu/3779/|access-date = 2022-02-21|archive-date = 2022-06-18|archive-url = https://web.archive.org/web/20220618111715/https://authors.library.caltech.edu/3779/|url-status = dead}}</ref> (in their scheme, spin is plotted against mass squared on a so-called [[Chew–Frautschi plot]]), which implied that the scattering of these particles would have very strange behavior&mdash;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.

In 1967, a notable step forward in the bootstrap approach was the principle of [[DHS duality]] introduced by [[Richard Dolen]], [[David Horn (Israeli physicist)|David Horn]], and [[Christoph Schmid (physicist)|Christoph Schmid]] in 1967,<ref>{{cite journal | last1 = Dolen | first1 = R. | last2 = Horn | first2 = D. | last3 = Schmid | first3 = C. | year = 1967 | title = Prediction of Regge-parameters of rho poles from low-energy pi-N scattering data | journal = Physical Review Letters | volume = 19 | issue = 7| pages = 402–407 | doi=10.1103/physrevlett.19.402| bibcode = 1967PhRvL..19..402D }}</ref> at [[Caltech]] (the original term for it was "average duality" or "finite energy sum rule (FESR) duality"). The three researchers noticed that [[Regge pole]] exchange (at high energy) and resonance (at low energy) descriptions offer multiple representations/approximations of one and the same physically observable process.<ref>Rickles 2014, pp. 38–9.</ref>

==1968–1974: Dual resonance model==
The first model in which hadronic particles essentially follow the Regge trajectories was the [[dual resonance model]] that was constructed by [[Gabriele Veneziano]] in 1968,<ref>{{cite journal | last1 = Veneziano | first1 = G | year = 1968 | title = Construction of a crossing-symmetric, Reggeon-behaved amplitude for linearly rising trajectories | url = https://cds.cern.ch/record/390478| journal = [[Il Nuovo Cimento A]] | volume = 57 | issue = 1| pages = 190–197 | bibcode = 1968NCimA..57..190V | doi = 10.1007/BF02824451 | s2cid = 121211496 }}</ref> who noted that the [[Leonhard Euler|Euler]] [[beta function]] could be used to describe 4-particle scattering amplitude data for such particles. The [[Veneziano scattering amplitude]] (or Veneziano model) was quickly generalized to an ''N''-particle amplitude by [[Ziro Koba]] and [[Holger Bech Nielsen]]<ref>{{cite journal | last1 = Koba | first1 = Z. | last2 = Nielsen | first2 = H. | year = 1969 | title = Reaction amplitude for N-mesons: A generalization of the Veneziano-Bardakçi-Ruegg-Virasoro model | journal = Nuclear Physics B | volume = 10 | issue = 4| pages = 633–655 | bibcode = 1969NuPhB..10..633K | doi = 10.1016/0550-3213(69)90331-9 }}</ref> (their approach was dubbed the [[Koba–Nielsen formalism]]), and to what are now recognized as closed strings by [[Miguel Ángel Virasoro (physicist)|Miguel Virasoro]]<ref>{{cite journal | last1 = Virasoro | first1 = M | year = 1969 | title = Alternative constructions of crossing-symmetric amplitudes with Regge behavior | journal = Physical Review | volume = 177 | issue = 5| pages = 2309–2311 | doi=10.1103/physrev.177.2309| bibcode = 1969PhRv..177.2309V}}</ref> and [[Joel A. Shapiro]]<ref>{{cite journal | last1 = Shapiro | first1 = J. A. | year = 1970 | title = Electrostatic analogue for the Virasoro model | journal = Physics Letters B | volume = 33 | issue = 5| pages = 361–362 | bibcode = 1970PhLB...33..361S | doi = 10.1016/0370-2693(70)90255-8 }}</ref> (their approach was dubbed the [[Shapiro–Virasoro model]]).

In 1969, the [[Chan–Paton rules]] (proposed by [[Jack Paton (physicist)|Jack E. Paton]] and [[Hong-Mo Chan]])<ref>{{cite journal | last1 = Chan | first1 = H. M. | last2 = Paton | first2 = J. E. | year = 1969 | title = Generalized Veneziano Model with Isospin | url = https://cds.cern.ch/record/349893| journal = Nucl. Phys. B| volume = 10 | issue = 3| page = 516 | bibcode = 1969NuPhB..10..516P| doi = 10.1016/0550-3213(69)90038-8}}</ref> enabled [[isospin]] factors to be added to the Veneziano model.<ref>Rickles 2014, p. 5.</ref>

In 1969–70, [[Yoichiro Nambu]],<ref>Nambu, Y. (1970). "Quark model and the factorization of the Veneziano amplitude." In R. Chand (ed.), ''Symmetries and Quark Models: Proceedings of the International Conference held at Wayne State University, Detroit, Michigan, June 18–20, 1969'' (pp. 269–277). Singapore: World Scientific.</ref> [[Holger Bech Nielsen]],<ref>Nielsen, H. B. "An almost physical interpretation of the dual N point function." [[Nordita]] preprint (1969); unpublished.</ref> and [[Leonard Susskind]]<ref>{{cite journal | last1 = Susskind | first1 = L | year = 1969 | title = Harmonic oscillator analogy for the Veneziano amplitude | journal = Physical Review Letters | volume = 23 | issue = 10| pages = 545–547 | doi=10.1103/physrevlett.23.545| bibcode = 1969PhRvL..23..545S}}</ref><ref>{{cite journal | last1 = Susskind | first1 = L | year = 1970 | title = Structure of hadrons implied by duality | journal = Physical Review D | volume = 1 | issue = 4| pages = 1182–1186 | doi=10.1103/physrevd.1.1182| bibcode = 1970PhRvD...1.1182S}}</ref> presented a physical interpretation of the Veneziano amplitude 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.

In 1971, [[Pierre Ramond]]<ref>{{cite journal | last1 = Ramond | first1 = P. | year = 1971 | title = Dual Theory for Free Fermions | journal = Phys. Rev. D | volume = 3 | issue = 10| page = 2415 | bibcode = 1971PhRvD...3.2415R | doi = 10.1103/PhysRevD.3.2415 }}</ref> and, independently, [[John H. Schwarz]] and [[André Neveu]]<ref>{{cite journal | last1 = Neveu | first1 = A. | last2 = Schwarz | first2 = J. | year = 1971 | title = Tachyon-free dual model with a positive-intercept trajectory | journal = Physics Letters | volume = 34B | issue = 6| pages = 517–518 | bibcode = 1971PhLB...34..517N | doi = 10.1016/0370-2693(71)90669-1 }}</ref> attempted to implement fermions into the dual model. This led to the concept of "spinning strings", and pointed the way to a method for removing the problematic [[tachyon]] (see [[RNS formalism]]).<ref>Rickles 2014, p. 97.</ref>

Dual resonance models for strong interactions were a relatively popular subject of study between 1968 and 1973.<ref>Rickles 2014, pp. 5–6, 44.</ref> The scientific community lost interest in string theory as a theory of strong interactions in 1973 when [[quantum chromodynamics]] became the main focus of theoretical research<ref>Rickles 2014, p. 77.</ref> (mainly due to the theoretical appeal of its [[asymptotic freedom]]).<ref>Rickles 2014, p. 11 n. 22.</ref>

==1974–1984: Bosonic string theory and superstring theory==

In 1974, John H. Schwarz and [[Joël Scherk]],<ref>{{cite journal | last1 = Scherk | first1 = J. |author-link1=Joël Scherk | last2 = Schwarz | first2 = J. | year = 1974 | title = Dual models for non-hadrons | journal = Nuclear Physics B | volume = 81 | issue = 1| pages = 118–144 | bibcode = 1974NuPhB..81..118S | doi = 10.1016/0550-3213(74)90010-8 }}</ref> and independently [[Tamiaki Yoneya]],<ref>{{cite journal | last1 = Yoneya | first1 = T. | year = 1974 | title = Connection of dual models to electrodynamics and gravidynamics | journal = Progress of Theoretical Physics | volume = 51 | issue = 6| pages = 1907–1920 | doi=10.1143/ptp.51.1907| bibcode = 1974PThPh..51.1907Y| doi-access = free }}</ref> 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]].

String theory is formulated in terms of the [[Polyakov action]],<ref>[[Barton Zwiebach|Zwiebach, Barton]] (2009). ''A First Course in String Theory''. Cambridge University Press. p. 582.</ref> which describes how strings move through space and time. Like springs, the strings tend 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 "[[Musical note|note]]" the string "sounds." The scale of notes, each corresponding to a different kind of particle, is termed the "[[energy spectrum|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 has several problems: it has a [[critical dimension]] ''D'' = 26, a feature that was originally discovered by [[Claud Lovelace]] in 1971;<ref>{{citation|last=Lovelace|first=Claud|title=Pomeron form factors and dual Regge cuts|journal=Physics Letters B|volume=34|issue=6|year=1971|pages=500–506|bibcode=1971PhLB...34..500L|doi=10.1016/0370-2693(71)90665-4}}.</ref> the theory has a fundamental instability, the presence of tachyons<ref>Sakata, Fumihiko; Wu, Ke; Zhao, En-Guang (eds.), ''Frontiers of Theoretical Physics: A General View of Theoretical Physics at the Crossing of Centuries'', World Scientific, 2001, p. 121.</ref> (see [[tachyon condensation]]); additionally, 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]] (in [[Western world|the West]])<ref>Rickles 2014, p. 104.</ref> in 1971,<ref>[[Jean-Loup Gervais|J. L. Gervais]] and [[Bunji Sakita|B. Sakita]] worked on the two-dimensional case in which they use the concept of "supergauge," taken from Ramond, Neveu, and Schwarz's work on dual models: {{Cite journal | last1 = Gervais | first1 = J.-L. | last2 = Sakita | first2 = B. | doi = 10.1016/0550-3213(71)90351-8 | title = Field theory interpretation of supergauges in dual models | journal = Nuclear Physics B | volume = 34 | issue = 2 | pages = 632–639 | year = 1971 |bibcode = 1971NuPhB..34..632G }}</ref> a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as [[superstring theory|superstring theories]].

In 1977, the [[GSO projection]] (named after [[Ferdinando Gliozzi]], Joël Scherk, and [[David I. Olive]]) led to a family of tachyon-free unitary free string theories,<ref>{{cite journal | last1 = Gliozzi | first1 = F. | last2 = Scherk | first2 = J. | last3 = Olive | first3 = D. I. | year = 1977 | title = Supersymmetry, Supergravity Theories and the Dual Spinor Model | url = https://cds.cern.ch/record/203097| journal = Nucl. Phys. B | volume = 122 | issue = 2| page = 253 | doi=10.1016/0550-3213(77)90206-1| bibcode = 1977NuPhB.122..253G }}</ref> the first consistent superstring theories (see [[#1984–1994: first superstring revolution|below]]).

==1984–1994: First superstring revolution<!--'First superstring revolution' and 'First Superstring Revolution' redirect here-->==
The '''first superstring revolution'''<!--boldface per WP:R#PLA--> is a period of important discoveries that began in 1984.<ref>Rickles 2014, p. 147: "Green and Schwarz's anomaly cancellation paper triggered a very large increase in the production of papers on the subject, including a related pair of papers that between them had the potential to provide the foundation for a realistic [[unified theory]] of both particle physics and gravity."</ref> It was realized that string theory was capable of describing all [[elementary particle]]s as well as the [[fundamental interactions|interactions]] between them. Hundreds of physicists started to work on [[string theory]] as the most promising idea to unify physical theories.<ref>Rickles 2014, p. 157.</ref> The revolution was started by a discovery of [[Anomaly (physics)|anomaly cancellation]] in [[type I string theory]] via the [[Green–Schwarz mechanism]] (named after [[Michael Green (physicist)|Michael Green]] and John H. Schwarz) in 1984.<ref>{{Cite journal | last1 = Green | first1 = M. B. | last2 = Schwarz | first2 = J. H. | doi = 10.1016/0370-2693(84)91565-X | title = Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory | journal = Physics Letters B | volume = 149 | issue = 1–3 | pages = 117–122 | year = 1984 |bibcode = 1984PhLB..149..117G }}</ref><ref>[[Clifford V. Johnson|Johnson, Clifford V.]] ''D-branes''. Cambridge University Press. 2006, pp. 169–70.</ref> The ground-breaking discovery of the [[Heterotic string theory|heterotic string]] was made by [[David Gross]], [[Jeffrey A. Harvey|Jeffrey Harvey]], [[Emil Martinec]], and [[Ryan Rohm]] in 1985.<ref name=GHMR>{{cite journal | last1 = Gross | first1 = D. J. | last2 = Harvey | first2 = J. A. | last3 = Martinec | first3 = E. | last4 = Rohm | first4 = R. | year = 1985 | title = Heterotic string | journal = Physical Review Letters | volume = 54 | issue = 6| pages = 502–505 | doi=10.1103/physrevlett.54.502| pmid = 10031535 | bibcode = 1985PhRvL..54..502G }}</ref> It was also realized by [[Philip Candelas]], [[Gary Horowitz]], [[Andrew Strominger]], and [[Edward Witten]] in 1985 that to obtain <math>N=1</math> [[supersymmetry]], the six small extra dimensions (the ''D'' = 10 critical dimension of superstring theory had been originally discovered by John H. Schwarz in 1972)<ref>{{cite journal | last1 = Schwarz | first1 = J. H. | year = 1972 | title = Physical states and pomeron poles in the dual pion model | journal = Nuclear Physics B | volume = 46 | issue = 1| pages = 61–74 | bibcode = 1972NuPhB..46...61S | doi = 10.1016/0550-3213(72)90201-5 }}</ref> need to be [[Compactification (physics)|compactified]] on a [[Calabi–Yau manifold]].<ref>{{cite journal | last1 = Candelas | first1 = P. | last2 = Horowitz | first2 = G. | last3 = Strominger | first3 = A. | last4 = Witten | first4 = E. | year = 1985 | title = Vacuum configurations for superstrings | journal = Nuclear Physics B | volume = 258 | pages = 46–74 | bibcode = 1985NuPhB.258...46C | doi = 10.1016/0550-3213(85)90602-9 }}</ref> (In string theory, compactification is a generalization of [[Kaluza–Klein theory]], which was first proposed in the 1920s.)<ref>Rickles 2014, p. 89 n. 44.</ref>

By 1985, five separate superstring theories had been described: type I,<ref name=GS82>Green, M. B., Schwarz, J. H. (1982). "Supersymmetrical string theories." ''Physics Letters B'', '''109''', 444–448 (this paper classified the consistent ten-dimensional superstring theories and gave them the names Type I, Type IIA, and Type IIB).</ref> [[Type II string theory|type II (IIA and IIB)]],<ref name=GS82/> and [[Heterotic string theory|heterotic {{Smaller|(SO(32) and ''E''<sub>8</sub>×''E''<sub>8</sub>)}}]].<ref name=GHMR/>

''[[Discover (magazine)|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.

In 1987, {{Interlanguage link|Eric Bergshoeff|de}}, {{Interlanguage link|Ergin Sezgin|de}} and [[Paul Townsend]] showed that there are no superstrings in eleven dimensions (the largest number of dimensions consistent with a single graviton in [[supergravity]] theories),<ref>{{Cite journal|last=Nahm|first=W.|date=1978-03-27|title=Supersymmetries and their representations|url=https://dx.doi.org/10.1016/0550-3213%2878%2990218-3|journal=Nuclear Physics B|language=en|volume=135|issue=1|pages=149–166|doi=10.1016/0550-3213(78)90218-3|bibcode=1978NuPhB.135..149N |issn=0550-3213}}</ref> but [[supermembranes]].<ref>E. Bergshoeff, E. Sezgin, P. K. Townsend, "Supermembranes and Eleven-Dimensional Supergravity," ''Phys. Lett. B'' '''189''': 75 (1987).</ref>

==1994–2003: Second superstring revolution<!--'Second superstring revolution' and 'Second Superstring Revolution' redirect here-->==
In the early 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an 11-dimensional theory<ref>It was [[Edward Witten]] who observed that the theory must be an 11-dimensional one in {{cite journal |last1=Witten |first1=Edward |date=1995 |title=String theory dynamics in various dimensions |journal=Nuclear Physics B |volume=443 |issue=1 |pages=85–126 |doi=10.1016/0550-3213(95)00158-O|arxiv = hep-th/9503124 |bibcode = 1995NuPhB.443...85W |s2cid=16790997 }}</ref><ref>{{cite journal |last1=Duff |author-link=Michael Duff (physicist) |first1=Michael |date=1998 |title=The theory formerly known as strings |journal=Scientific American |volume=278 |issue=2 |pages=64–9 |doi=10.1038/scientificamerican0298-64|bibcode=1998SciAm.278b..64D }}</ref> that became known as [[M-theory]] (for details, see [[Introduction to M-theory]]).<ref>When Witten named it M-theory, he did not specify what the "M" stood for, presumably because he did not feel he had the right to name a theory he had not been able to fully describe. The "M" sometimes is said to stand for Mystery, or Magic, or Mother. More serious suggestions include Matrix or Membrane. [[Sheldon Glashow]] has noted that the "M" might be an upside down "W", standing for Witten. Others have suggested that the "M" in M-theory should stand for Missing, Monstrous or even Murky. According to Witten himself, as quoted in the [https://www.pbs.org/wgbh/nova/series/the-elegant-universe/ PBS documentary] based on [[Brian Greene]]'s ''[[The Elegant Universe]]'', the "M" in M-theory stands for "magic, mystery, or matrix according to taste."</ref> These discoveries sparked the '''second superstring revolution'''<!--boldface per WP:R#PLA--> that took place approximately between 1994 and 1995.<ref>Rickles 2014, p. 208 n. 2.</ref>

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 (string theory)|mirror symmetry]], and [[conifold]] transitions. The different theories of strings were also related to M-theory.

In 1995, [[Joseph Polchinski]] discovered that the theory requires the inclusion of higher-dimensional objects, called [[D-brane]]s:<ref>{{cite journal | last1 = Polchinski | first1 = J | year = 1995 | title = Dirichlet branes and Ramond-Ramond charges | journal = Physical Review D | volume = 50 | issue = 10| pages = R6041–R6045 | bibcode = 1995PhRvL..75.4724P | doi = 10.1103/PhysRevLett.75.4724 | pmid = 10059981 | arxiv = hep-th/9510017 | s2cid = 4671529 }}</ref> these are the sources of electric and magnetic [[Ramond–Ramond field]]s that are required by [[string duality]].<ref>Rickles 2014, p. 212.</ref> D-branes added additional rich mathematical structure to the theory, and opened possibilities for constructing realistic cosmological models in the theory (for details, see [[Brane cosmology]]).

In 1997–98, [[Juan Maldacena]] conjectured a relationship between [[type IIB string theory]] and [[N = 4 supersymmetric Yang–Mills theory|''N'' = 4 supersymmetric Yang–Mills theory]], a [[gauge theory]].<ref>{{cite journal | last1=Maldacena| first1=Juan | title=The Large N limit of superconformal field theories and supergravity | journal=Advances in Theoretical and Mathematical Physics | volume=2 | issue=4 | year=1998 | pages=231–252 | arxiv=hep-th/9711200|bibcode = 1998AdTMP...2..231M | doi=10.4310/ATMP.1998.V2.N2.A1}}</ref> This conjecture, called the [[AdS/CFT correspondence]], has generated a great deal of interest in [[high energy physics]].<ref>Rickles 2014, p. 207.</ref> It is a realization of the [[holographic principle]], which has far-reaching implications: the AdS/CFT correspondence has helped elucidate the mysteries of [[black holes]] suggested by [[Stephen Hawking]]'s work<ref>Rickles 2014, p. 222.</ref> and is believed to provide a resolution of the [[black hole information paradox]].<ref>{{cite journal|title=The Illusion of Gravity |last=Maldacena |first=Juan |year=2005 |journal=Scientific American |url=http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf |bibcode=2005SciAm.293e..56M |volume=293 |pages=56–63 |doi=10.1038/scientificamerican1105-56 |issue=5 |pmid=16318027 |url-status=dead |archive-url=https://web.archive.org/web/20131110061237/http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf |archive-date=2013-11-10 }} (p. 63.)</ref>

==2003–present==
{{Update section|date=August 2023|reason=any noteworthy developments over the last 20 years?}}
In 2003, [[Michael R. Douglas]]'s discovery of the [[string theory landscape]],<ref>Douglas, Michael R., "The statistics of string / M theory vacua", ''JHEP'' '''0305''', 46 (2003). {{arxiv|hep-th/0303194}}</ref> which suggests that string theory has a large number of inequivalent [[False vacuum|false vacua]],<ref>The most commonly quoted number is of the order 10<sup>500</sup>. See: Ashok S., Douglas, M., "Counting flux vacua", ''JHEP'' '''0401''', 060 (2004).</ref> led to much discussion of what string theory might eventually be expected to predict, and how [[cosmology]] can be incorporated into the theory.<ref>Rickles 2014, pp. 230–5 and 236 n. 63.</ref>

A possible mechanism of string theory vacuum stabilization (the [[KKLT mechanism]]) was proposed in 2003 by [[Shamit Kachru]], [[Renata Kallosh]], [[Andrei Linde]], and [[Sandip Trivedi]].<ref>{{cite journal|title=de Sitter Vacua in String Theory|journal=Physical Review D|volume=68|issue=4|pages=046005|arxiv=hep-th/0301240|author=Kachru, Shamit|author2=Kallosh, Renata|author3=Linde, Andrei|author4=Trivedi, Sandip P.|year=2003|doi=10.1103/PhysRevD.68.046005|bibcode=2003PhRvD..68d6005K|s2cid=119482182}}</ref>
Much of the present-day research is focused on characterizing the "[[Swampland (physics)|swampland]]" of theories incompatible with [[quantum gravity]]. The [[Ryu–Takayanagi conjecture]] introduced many concepts from quantum information into string theory.

==See also==
* [[History of quantum field theory]]
* [[History of loop quantum gravity]]
* [[Strings (conference)]]

==Notes==
{{reflist|22em}}

==References==
*{{cite book|author=Rickles|first=Dean|date=2014|title=A Brief History of String Theory: From Dual Models to M-Theory|publisher=Springer|isbn=978-3-642-45128-7|author-link=Dean Rickles}}

==Further reading==
*{{cite book
 | author=Paul Frampton
 | date = 1974
 | title = Dual Resonance Models
 | publisher = Frontiers in Physics, W. A. Benjamin
 | isbn = 978-0-8053-2581-2
| author-link = Paul Frampton
 }}
*{{cite arXiv
 | author = Joel A. Shapiro 
 | date = 2007
 | title = Reminiscence on the Birth of String Theory
 | eprint = 0711.3448
| class = hep-th
 }}
*{{cite arXiv
 | author = John H. Schwarz
 | date = 2012
 | title = The Early History of String Theory and Supersymmetry
 | eprint = 1201.0981
| class = physics.hist-ph
 | author-link = John Henry Schwarz
 }}
*{{cite book
 | author=Andrea Cappelli
 | author2=Elena Castellani
 | author3=Filippo Colomo
 | author4-link=Paolo Di Vecchia
 | author4=Paolo Di Vecchia
 | date=2012
 | title=The Birth of String Theory
 | publisher=Cambridge University Press
 | isbn=978-0-521-19790-8
}}

{{String theory topics |state=collapsed}}
{{History of physics}}

[[Category:String theory]]
[[Category:History of physics]]