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. 'Superstring theory' is a shorthand for
supersymmetric string theory because unlike bosonic string theory, it is the
version of string theory that incorporates fermions and supersymmetry.
Since the second superstring revolution the five superstring theories are
regarded as different limits of a single theory tentatively called M-theory, or
simply string theory. Background
The deepest problem in theoretical physics is harmonizing the theory of
general relativity, which describes gravitation and applies to large-scale
structures, with quantum mechanics, which describes the other three
fundamental forces acting on the atomic scale.
The development of a quantum field theory of a force invariably results in
infinite possibilities. Physicists have developed mathematical techniques to
eliminate these infinities which work for three of the four fundamental
forces—electromagnetic, strong nuclear and weak nuclear forces—but not for
gravity. The development of a quantum theory of gravity must therefore come
about by different means than those used for the other forces.
According to the theory, the fundamental constituents of reality are strings of
the Planck length which vibrate at resonant frequencies. Every string, in
theory, has a unique resonance, or harmonic. Different harmonics determine
different fundamental particles. The tension in a string is on the order of
the Planck force. The graviton, for example, is predicted by the theory to
be a string with wave amplitude zero. = Lack of experimental evidence=
Superstring theory is based on supersymmetry. No supersymmetric
particles have been discovered and recent research at LHC and Tevatron has
excluded some of the ranges. For instance, the mass constraint of the
Minimal Supersymmetric Standard Model squarks has been up to 1.1 TeV, and
gluinos up to 500 GeV. No report on suggesting large extra dimensions has
been delivered from LHC. There have been no principles so far to limit the number
of vacua in the concept of a landscape of vacua.
Some particle physicists became disappointed by the lack of experimental
verification of supersymmetry, and some have already discarded it; Jon
Butterworth at the University College London said that we had no sign of
supersymmetry, even in higher energy region, excluding the superpartners of
the top quark up to a few TeV. Ben Allanach at the University of Cambridge
states that if we do not discover any new particles in the next trial at the
LHC, then we can say it is unlikely to discover supersymmetry at CERN in the
foreseeable future. Extra dimensions
See also: Why does consistency require 10 dimensions?
Our physical space is observed to have only three large dimensions and—taken
together with duration as the fourth dimension—a physical theory must take
this into account. However, nothing prevents a theory from including more
than 4 dimensions. In the case of string theory, consistency requires spacetime
to have 10 dimensions. The fact that we see only 3 dimensions of space can be
explained by one of two mechanisms: either the extra dimensions are
compactified on a very small scale, or else our world may live on a
3-dimensional submanifold corresponding to a brane, on which all known particles
besides gravity would be restricted. If the extra dimensions are
compactified, then the extra six dimensions must be in the form of a
Calabi–Yau manifold. Within the more complete framework of M-theory, they
would have to take form of a G2 manifold. Calabi-Yaus are interesting
mathematical spaces in their own right. A particular exact symmetry of
string/M-theory called T-duality, has led to the discovery of equivalences
between different Calabi-Yaus called Mirror Symmetry.
Superstring theory is not the first theory to propose extra spatial
dimensions. It can be seen as building upon the Kaluza–Klein theory which
proposed a 4+1-dimensional theory of gravity. When compactified on a circle,
the gravity in the extra dimension precisely describes electromagnetism
from the perspective of the 3 remaining large space dimensions. Thus the
original Kaluza–Klein theory is a prototype for the unification of gauge
and gravity interactions, at least at the classical level, however it is known
to be insufficient to describe nature for a variety of reasons A more complex
compact geometry is needed to reproduce the known gauge forces. This is not all:
In order to obtain a consistent, fundamental, quantum theory the upgrade
to string theory is also necessary, not just the extra dimensions.
Number of superstring theories Theoretical physicists were troubled by
the existence of five separate string theories. A possible solution for this
dilemma was suggested at the beginning of what is called the second superstring
revolution in the 1990s, which suggests that the five string theories might be
different limits of a single underlying theory, called M-theory. This remains a
conjecture. The five consistent superstring theories
are: The type I string has one supersymmetry
in the ten-dimensional sense. This theory is special in the sense that it
is based on unoriented open and closed strings, while the rest are based on
oriented closed strings. The type II string theories have two
supersymmetries in the ten-dimensional sense. There are actually two kinds of
type II strings called type IIA and type IIB. They differ mainly in the fact that
the IIA theory is non-chiral while the IIB theory is chiral.
The heterotic string theories are based on a peculiar hybrid of a type I
superstring and a bosonic string. There are two kinds of heterotic strings
differing in their ten-dimensional gauge groups: the heterotic E8×E8 string and
the heterotic SO(32) string. is slightly inaccurate since among the SO(32) Lie
groups, string theory singles out a quotient Spin(32)/Z2 that is not
equivalent to SO(32).) Chiral gauge theories can be
inconsistent due to anomalies. This happens when certain one-loop Feynman
diagrams cause a quantum mechanical breakdown of the gauge symmetry. The
anomalies were canceled out via the Green–Schwarz mechanism.
Even though there are only five superstring theories, in order to make
detailed predictions for real experiments, information is needed about
exactly what physical configuration the theory is in. This considerably
complicates efforts to test string theory because there is an
astronomically high number – 10500 or more – of configurations that meet some
of the basic requirements to be consistent with our world. Along with
the extreme remoteness of the Planck scale, this is the other major reason it
is hard to test superstring theory. Another approach to the number of
superstring theories refers to the mathematical structure called
composition algebra. In the findings of abstract algebra there are just seven
composition algebras over the field of real numbers. In 1990 physicists R. Foot
and G.C. Joshi in Australia stated that "the seven classical superstring
theories are in one-to-one correspondence to the seven composition
algebras." Integrating general relativity and
quantum mechanics General relativity typically deals with
situations involving large mass objects in fairly large regions of spacetime
whereas quantum mechanics is generally reserved for scenarios at the atomic
scale. The two are very rarely used together, and the most common case in
which they are combined is in the study of black holes. Having "peak density",
or the maximum amount of matter possible in a space, and very small area, the two
must be used in synchrony in order to predict conditions in such places; yet,
when used together, the equations fall apart, spitting out impossible answers,
such as imaginary distances and less than one dimension.
The major problem with their congruence is that, at Planck scale lengths,
general relativity predicts a smooth, flowing surface, while quantum mechanics
predicts a random, warped surface, neither of which are anywhere near
compatible. Superstring theory resolves this issue, replacing the classical idea
of point particles with loops. These loops have an average diameter of the
Planck length, with extremely small variances, which completely ignores the
quantum mechanical predictions of Planck-scale length dimensional warping.
Singularities are avoided because the observed consequences of "Big Crunches"
never reach zero size. In fact, should the universe begin a "big crunch" sort
of process, string theory dictates that the universe could never be smaller than
the size of a string, at which point it would actually begin expanding.
Mathematics = D-branes=
D-branes are membrane-like objects in 10D string theory. They can be thought
of as occurring as a result of a Kaluza–Klein compactification of 11D
M-theory which contains membranes. Because compactification of a geometric
theory produces extra vector fields the D-branes can be included in the action
by adding an extra U(1) vector field to the string action.
In type I open string theory, the ends of open strings are always attached to
D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge
fields would then correspond to the compactification of some
higher-dimensional theory above 11 dimensions which is not thought to be
possible to date. Furthemore, the tachyons attached to the D-branes, show,
the instability of those d-branes with respect to the annihilation.We will
consider that tachyon total energy is the total energy of the D-branes.
= Why five superstring theories?= For a 10 dimensional supersymmetric
theory we are allowed a 32-component Majorana spinor. This can be decomposed
into a pair of 16-component Majorana-Weyl spinors. There are then
various ways to construct an invariant depending on whether these two spinors
have the same or opposite chiralities: The heterotic superstrings come in two
types SO(32) and E8×E8 as indicated above and the type I superstrings
include open strings. Beyond superstring theory
It is conceivable that the five superstring theories are approximated to
a theory in higher dimensions possibly involving membranes. Because the action
for this involves quartic terms and higher so is not Gaussian, the
functional integrals are very difficult to solve and so this has confounded the
top theoretical physicists. Edward Witten has popularised the concept of a
theory in 11 dimensions M-theory involving membranes interpolating from
the known symmetries of superstring theory. It may turn out that there exist
membrane models or other non-membrane models in higher dimensions which may
become acceptable when new unknown symmetries of nature are found, such as
noncommutative geometry for example. It is thought, however, that 16 is probably
the maximum since O(16) is a maximal subgroup of E8 the largest exceptional
lie group and also is more than large enough to contain the Standard Model.
Quartic integrals of the non-functional kind are easier to solve so there is
hope for the future. This is the series solution which is always convergent when
a is non-zero and negative: In the case of membranes the series
would correspond to sums of various membrane interactions that are not seen
in string theory. = Compactification=
Investigating theories of higher dimensions often involves looking at the
10 dimensional superstring theory and interpreting some of the more obscure
results in terms of compactified dimensions. For example, D-branes are
seen as compactified membranes from 11D M-theory. Theories of higher dimensions
such as 12D F-theory and beyond will produce other effects such as gauge
terms higher than U(1). The components of the extra vector fields in the
D-brane actions can be thought of as extra coordinates in disguise. However,
the known symmetries including supersymmetry currently restrict the
spinors to have 32-components which limits the number of dimensions to 11
Some commentators have speculated that the exceptional lie groups E6, E7 and E8
having maximum orthogonal subgroups O(10), O(12) and O(16) may be related to
theories in 10, 12 and 16 dimensions; 10 dimensions corresponding to string
theory and the 12 and 16 dimensional theories being yet undiscovered but
would be theories based on 3-branes and 7-branes respectively. However this is a
minority view within the string community. Since E7 is in some sense F4
quaternified and E8 is F4 octonified, then the 12 and 16 dimensional theories,
if they did exist, may involve the noncommutative geometry based on the
quaternions and octonions respectively. From the above discussion, it can be
seen that physicists have many ideas for extending superstring theory beyond the
current 10 dimensional theory, but so far none have been successful.
= Kac–Moody algebras= Since strings can have an infinite
number of modes, the symmetry used to describe string theory is based on
infinite dimensional Lie algebras. Some Kac–Moody algebras that have been
considered as symmetries for M-theory have been E10 and E11 and their
supersymmetric extensions. See also
AdS/CFT dS/CFT correspondence
Grand unification theory Large Hadron Collider
List of string theory topics Quantum gravity
String field theory Notes
References External links
Wellcome Collection video on superstring theory
The Official Superstring theory website: http:superstringtheory.com/index.html