History of string theory
String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. The following attempts to be a concise history of the discipline.
String theory is an outgrowth of a research program begun by Werner Heisenberg 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 theneutron were not pointlike particles like the electron. Their magnetic moment differed greatly from that of a pointlike spin-1/2 charged particle, 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.
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 proton, the neutron and the Lambda (see Sakata model), Geoffrey 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 mesons 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 model, 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 byMiguel Virasoro 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 Nambu, 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 whenquantum 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 fermions 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.
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 particles as well as the interactionsbetween 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.
1994–2000: second superstring revolution
In the early 1990s, Edward Witten 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 thesecond 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-branes. 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 holes, locality and information in physics, as well as the nature of the gravitational interaction.
In the 2000s, the discovery of the string theory landscape, 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.
- 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 PBS documentary based on Brian Greene‘s The Elegant Universe, the “M” in M-theory stands for “magic, mystery, or matrix according to taste.”
- Paul Frampton (1974). Dual Resonance Models. Frontiers in Physics. ISBN 0-8053-2581-6.
- Shapiro, Joel A. (2007). “Reminiscence on the Birth of String Theory”. arXiv:0711.3448.
- Andrea Cappelli; Elena Castellani, Filippo Colomo, Paolo Di Vecchia (2012). The Birth of String Theory. Cambridge University Press. ISBN 978-0-521-19790-8.