Thehistory 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 toquantum gravity,particle andcondensed matter physics,cosmology, andpure mathematics.
String theory represents an outgrowth ofS-matrix theory,[1] a research program begun byWerner Heisenberg in 1943[2] followingJohn Archibald Wheeler's 1937 introduction of the S-matrix.[3] 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[4] and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and becausequantum chromodynamics supplanted it as an experimentally better-qualified approach to thestrong interactions.[5]
The theory presented a radical rethinking of the foundations of physical laws. By the 1940s it had become clear that theproton and theneutron were not pointlike particles like the electron. Theirmagnetic moment differed greatly from that of a pointlikespin-½ charged particle, too much to attribute the difference to a smallperturbation. 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—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 thequantum mechanicalamplitude 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.
TheS-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. Inquantum 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 useunitarity 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 aperturbation 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 whenMurray Gell-Mann recognized thatdispersion relations—like those discovered byHendrik Kramers andRalph Kronig in the 1920s (seeKramers–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.[6] The dispersion relations wereanalytic properties of the S-matrix,[7] and they imposed more stringent conditions than those that follow from unitarity alone. This development in S-matrix theory stemmed from Murray Gell-Mann andMarvin Leonard Goldberger's (1954) discovery ofcrossing symmetry, another condition that the S-matrix had to fulfil.[8][7]
Prominent advocates of the new "dispersion relations" approach includedStanley Mandelstam[9] andGeoffrey Chew,[10] both atUC Berkeley at the time. Mandelstam discovered thedouble dispersion relations, a new and powerful analytic form, in 1958,[9] and believed that it would provide the key to progress in the intractable strong interactions.
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 physicistShoichi Sakata proposed that the particles could be understood asbound states of just three of them (the proton, the neutron and theLambda; seeSakata model),[11] Geoffrey Chew believed that none of these particles are fundamental[12][13] (for details, seeBootstrap model). Sakata's approach was reworked in the 1960s into thequark model byMurray Gell-Mann andGeorge Zweig by making thecharges of the hypothetical constituentsfractional 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.
In 1959,Tullio Regge, a young theorist in Italy, discovered that bound states in quantum mechanics can be organized into families known asRegge trajectories, each family having distinctiveangular momenta.[14] This idea was generalized torelativistic quantum mechanics byStanley Mandelstam,Vladimir Gribov andMarcel Froissart, using a mathematical method (theSommerfeld–Watson representation) discovered decades earlier byArnold Sommerfeld andKenneth M. Watson: the result was dubbed theFroissart–Gribov formula.[15]
In 1961, Geoffrey Chew andSteven Frautschi recognized thatmesons had straight line Regge trajectories[16] (in their scheme, spin is plotted against mass squared on a so-calledChew–Frautschi plot), which implied 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 ofcomposite particles on Regge trajectories, whose scattering amplitudes had theasymptotic form demanded by Regge theory.
In 1967, a notable step forward in the bootstrap approach was the principle ofDHS duality introduced byRichard Dolen,David Horn, andChristoph Schmid in 1967,[17] atCaltech (the original term for it was "average duality" or "finite energy sum rule (FESR) duality"). The three researchers noticed thatRegge pole exchange (at high energy) and resonance (at low energy) descriptions offer multiple representations/approximations of one and the same physically observable process.[18]
The first model in which hadronic particles essentially follow the Regge trajectories was thedual resonance model that was constructed byGabriele Veneziano in 1968,[19] who noted that theEulerbeta function could be used to describe 4-particle scattering amplitude data for such particles. TheVeneziano scattering amplitude (or Veneziano model) was quickly generalized to anN-particle amplitude byZiro Koba andHolger Bech Nielsen[20] (their approach was dubbed theKoba–Nielsen formalism), and to what are now recognized as closed strings byMiguel Virasoro[21] andJoel A. Shapiro[22] (their approach was dubbed theShapiro–Virasoro model).
In 1969, theChan–Paton rules (proposed byJack E. Paton andHong-Mo Chan)[23] enabledisospin factors to be added to the Veneziano model.[24]
In 1969–70,Yoichiro Nambu,[25]Holger Bech Nielsen,[26] andLeonard Susskind[27][28] 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[29] and, independently,John H. Schwarz andAndré Neveu[30] 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 problematictachyon (seeRNS formalism).[31]
Dual resonance models for strong interactions were a relatively popular subject of study between 1968 and 1973.[32] The scientific community lost interest in string theory as a theory of strong interactions in 1973 whenquantum chromodynamics became the main focus of theoretical research[33] (mainly due to the theoretical appeal of itsasymptotic freedom).[34]
In 1974, John H. Schwarz andJoël Scherk,[35] and independentlyTamiaki Yoneya,[36] studied theboson-like patterns ofstring vibration and found that their properties exactly matched those of thegraviton, the gravitational force's hypotheticalmessenger particle. Schwarz and Scherk argued that string theory had failed to catch on because physicists had underestimated its scope. This led to the development ofbosonic string theory.
String theory is formulated in terms of thePolyakov action,[37] 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 ofquantum 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 bothopen strings, which have two distinct endpoints, andclosed 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 acritical dimensionD = 26, a feature that was originally discovered byClaud Lovelace in 1971;[38] the theory has a fundamental instability, the presence of tachyons[39] (seetachyon condensation); additionally, the spectrum of particles contains onlybosons, particles like thephoton 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 includefermions in its spectrum led to the invention ofsupersymmetry (inthe West)[40] in 1971,[41] a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known assuperstring theories.
In 1977, theGSO projection (named afterFerdinando Gliozzi, Joël Scherk, andDavid I. Olive) led to a family of tachyon-free unitary free string theories,[42] the first consistent superstring theories (seebelow).
Thefirst superstring revolution is a period of important discoveries that began in 1984.[43] It was realized that string theory was capable of describing allelementary particles as well as theinteractions between them. Hundreds of physicists started to work onstring theory as the most promising idea to unify physical theories.[44] The revolution was started by a discovery ofanomaly cancellation intype I string theory via theGreen–Schwarz mechanism (named afterMichael Green and John H. Schwarz) in 1984.[45][46] The ground-breaking discovery of theheterotic string was made byDavid Gross,Jeffrey Harvey,Emil Martinec, andRyan Rohm in 1985.[47] It was also realized byPhilip Candelas,Gary Horowitz,Andrew Strominger, andEdward Witten in 1985 that to obtainsupersymmetry, the six small extra dimensions (theD = 10 critical dimension of superstring theory had been originally discovered by John H. Schwarz in 1972)[48] need to becompactified on aCalabi–Yau manifold.[49] (In string theory, compactification is a generalization ofKaluza–Klein theory, which was first proposed in the 1920s.)[50]
By 1985, five separate superstring theories had been described: type I,[51]type II (IIA and IIB),[51] andheterotic(SO(32) andE8×E8).[47]
Discover magazine in the November 1986 issue (vol. 7, #11) featured a cover story written byGary Taubes, "Everything's Now Tied to Strings", which explained string theory for a popular audience.
In 1987,Eric Bergshoeff [de],Ergin Sezgin [de] andPaul Townsend showed that there are no superstrings in eleven dimensions (the largest number of dimensions consistent with a single graviton insupergravity theories),[52] butsupermembranes.[53]
In the early 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an 11-dimensional theory[54][55] that became known asM-theory (for details, seeIntroduction to M-theory).[56] These discoveries sparked thesecond superstring revolution that took place approximately between 1994 and 1995.[57]
The different versions ofsuperstring theory were unified, as long hoped, by new equivalences. These are known asS-duality,T-duality,U-duality,mirror symmetry, andconifold 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, calledD-branes:[58] these are the sources of electric and magneticRamond–Ramond fields that are required bystring duality.[59] D-branes added additional rich mathematical structure to the theory, and opened possibilities for constructing realistic cosmological models in the theory (for details, seeBrane cosmology).
In 1997–98,Juan Maldacena conjectured a relationship betweentype IIB string theory andN = 4 supersymmetric Yang–Mills theory, agauge theory.[60] This conjecture, called theAdS/CFT correspondence, has generated a great deal of interest inhigh energy physics.[61] It is a realization of theholographic principle, which has far-reaching implications: the AdS/CFT correspondence has helped elucidate the mysteries ofblack holes suggested byStephen Hawking's work[62] and is believed to provide a resolution of theblack hole information paradox.[63]
 | This section needs to beupdated. The reason given is: any noteworthy developments over the last 20 years?. Please help update this article to reflect recent events or newly available information.(August 2023) |
In 2003,Michael R. Douglas's discovery of thestring theory landscape,[64] which suggests that string theory has a large number of inequivalentfalse vacua,[65] led to much discussion of what string theory might eventually be expected to predict, and howcosmology can be incorporated into the theory.[66]
A possible mechanism of string theory vacuum stabilization (theKKLT mechanism) was proposed in 2003 byShamit Kachru,Renata Kallosh,Andrei Linde, andSandip Trivedi.[67]Much of the present-day research is focused on characterizing the "swampland" of theories incompatible withquantum gravity. TheRyu–Takayanagi conjecture introduced many concepts from quantum information into string theory.
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