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
and condensed matter physics, cosmology, and
pure mathematics.
== 1943–1959: S-matrix theory ==
String theory is an outgrowth of S-matrix
theory, a research program begun by Werner
Heisenberg in 1943 (following John Archibald
Wheeler's 1937 introduction of the S-matrix),
picked up and advocated by many prominent
theorists starting in the late 1950s and throughout
the 1960s, which was discarded and marginalized
in the mid 1970s to disappear by the 1980s.
It was forgotten because some of its mathematical
methods were alien, and because quantum chromodynamics
supplanted it as an experimentally better
qualified approach to the strong interactions.The
theory 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 differed greatly from that of a pointlike
spin-½ 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 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
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 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
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. He also recognized that
these relations might be useful in computing
observables for the case of strong interaction
physics. The dispersion relations were analytic
properties of the S-matrix, and they imposed
more stringent conditions than those that
follow from unitarity alone. This development
in S-matrix theory was based on Murray Gell-Mann
and Marvin Leonard Goldberger's (1954) discovery
of crossing symmetry, another condition that
the S-matrix had to fulfil.Prominent advocates
of the new "dispersion relations" approach
were Stanley Mandelstam and Geoffrey Chew,
both at UC Berkeley at the time. Mandelstam
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.
== 1959–1968: Regge theory and bootstrap
models ==
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 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
(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 charges of the hypothetical
constituents 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.
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 momenta. This idea was
generalized to relativistic quantum mechanics
by Mandelstam, Vladimir Gribov and Marcel
Froissart, using a mathematical method (the
Sommerfeld–Watson representation) discovered
decades earlier by Arnold Sommerfeld and Kenneth
Marshall Watson: the result was dubbed the
Froissart–Gribov formula.In 1961, Geoffrey
Chew and Steven Frautschi recognized that
mesons had straight line Regge trajectories
(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—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, and
Christoph Schmid in 1967, 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.
== 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, who noted that
the 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 (their approach was dubbed
the Koba–Nielsen formalism), and to what
are now recognized as closed strings by Miguel
Virasoro and Joel A. Shapiro (their approach
was dubbed the Shapiro–Virasoro model).
In 1969, the Chan–Paton rules (proposed
by Jack E. Paton and Hong-Mo Chan) enabled
isospin factors to be added to the Veneziano
model.In 1969–70, Yoichiro Nambu, Holger
Bech Nielsen, and Leonard Susskind 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 and, independently,
John H. Schwarz and André Neveu 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).Dual
resonance models for strong interactions were
a relatively popular subject of study between
1968 and 1973. 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
(mainly due to the theoretical appeal of its
asymptotic freedom).
== 1974–1984: bosonic string theory and
superstring theory ==
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.
String theory is formulated in terms of the
Polyakov action, 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 "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 has several problems:
it has a critical dimension D = 26, a feature
that was originally discovered by Claud Lovelace
in 1971; the theory has a fundamental instability,
the presence of tachyons (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 fermions in
its spectrum led to the invention of supersymmetry
(in the West) in 1971, a mathematical transformation
between bosons and fermions. String theories
that include fermionic vibrations are now
known as superstring theories.
In 1977, the GSO projection (named after Ferdinando
Gliozzi, Joel Scherk, and David I. Olive)
led to a family of tachyon-free unitary free
string theories, the first consistent superstring
theories (see below).
== 1984–1994: first superstring revolution
==
The first superstring revolution is a period
of important discoveries that began in 1984.
It was realized that string theory was capable
of describing all elementary particles 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
(named after Michael Green and John H. Schwarz)
in 1984. The ground-breaking discovery of
the heterotic string was made by David Gross,
Jeffrey Harvey, Emil Martinec, and Ryan Rohm
in 1985. It was also realized by Philip Candelas,
Gary Horowitz, Andrew Strominger, and Edward
Witten in 1985 that to obtain
N
=
1
{\displaystyle N=1}
supersymmetry, the six small extra dimensions
(the D = 10 critical dimension of superstring
theory had been originally discovered by John
H. Schwarz in 1972) need to be compactified
on a Calabi–Yau manifold. (In string theory,
compactification is a generalization of Kaluza–Klein
theory, which was first proposed in the 1920s.)By
1985, five separate superstring theories had
been described: type I, type II (IIA and IIB),
and heterotic (SO(32) and E8×E8).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, Eric Bergshoeff, Ergin Sezgin 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), but supermembranes.
== 1994–2003: second superstring revolution
==
In the early 1990s, Edward Witten and others
found strong evidence that the different superstring
theories were different limits of an 11-dimensional
theory that became known as M-theory (for
details, see Introduction to M-theory). These
discoveries sparked the second superstring
revolution that took place approximately between
1994 and 1995.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 related to M-theory.
In 1995, Joseph Polchinski discovered that
the theory requires the inclusion of higher-dimensional
objects, called D-branes: these are the sources
of electric and magnetic Ramond–Ramond fields
that are required by string duality. 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 string theory and N = 4
supersymmetric Yang–Mills theory, a gauge
theory. This conjecture, called the AdS/CFT
correspondence, has generated a great deal
of interest in high energy physics. 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 and is believed to provide a resolution
of the black hole information paradox.
== 2003–present ==
In 2003, Michael R. Douglas's discovery of
the string theory landscape, which suggests
that string theory has a large number of inequivalent
false vacua, led to much discussion of what
string theory might eventually be expected
to predict, and how cosmology can be incorporated
into the theory.
== See also ==
History of quantum field theory
History of loop quantum gravity
Pomerons in string theory
== Notes
