Superstring theory
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String theory |
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Fundamental objects |
Perturbative theory |
Non-perturbative results |
Phenomenology |
Mathematics |
Superstring theory is an
'Superstring theory' is a shorthand for supersymmetric string theory because unlike
Since the
Background
One of the deepest open problems in
Quantum field theory, in particular the
According to superstring theory, or more generally string theory, the fundamental constituents of reality are strings with radius on the order of the
History
Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry (in the West[clarification needed])[2] in 1971,[3] a mathematical transformation between bosons and fermions. String theories that include fermionic vibrations are now known as "superstring theories".
Since its beginnings in the seventies and through the combined efforts of many different researchers, superstring theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics.
Absence of physical evidence
Superstring theory is based on supersymmetry. No supersymmetric particles have been discovered and initial investigation, carried out in 2011 at the
Some particle physicists became disappointed by the lack of experimental verification of supersymmetry, and some have already discarded it.[11] Jon Butterworth at 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.[11]
Extra dimensions
Our
If the extra dimensions are compactified, then the extra 6 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. A particular exact symmetry of string/M-theory called T-duality (which exchanges momentum modes for winding number and sends compact dimensions of radius R to radius 1/R),[13] has led to the discovery of equivalences between different Calabi–Yau manifolds called mirror symmetry.
Superstring theory is not the first theory to propose extra spatial dimensions. It can be seen as building upon the
Number of superstring theories
Theoretical physicists were troubled by the existence of five separate superstring theories. A possible solution for this dilemma was suggested at the beginning of what is called the
String theories | |||||||
---|---|---|---|---|---|---|---|
Type | Spacetime dimensions
|
SUSY generators | chiral | open strings | heterotic compactification | gauge group
|
tachyon |
Bosonic (closed) | 26 | N = 0 | no | no | no | none | yes |
Bosonic (open) | 26 | N = 0 | no | yes | no | U(1) | yes |
I | 10 | N = (1,0) | yes | yes | no | SO(32) | no |
IIA | 10 | N = (1,1) | no | no | no | U(1) | no |
IIB | 10 | N = (2,0) | yes | no | no | none | no |
HO | 10 | N = (1,0) | yes | no | yes | SO(32) | no |
HE | 10 | N = (1,0) | yes | no | yes | E8 × E8 | no |
M-theory | 11 | N = 1 | no | no | no | none | no |
The five consistent superstring theories are:
- The closed strings, while the rest are based on oriented closed strings.
- The type II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). 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(parity conserving) while the IIB theory is chiral (parity violating).
- The SO(32) string. (The name heterotic SO(32) 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, making detailed predictions for real experiments requires information 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".[15]
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 (small spacetime regions). The two are very rarely used together, and the most common case that combines them 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 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 incongruence is that, at
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 one 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
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. Furthermore, the tachyons attached to the D-branes show the instability of those D-branes with respect to the annihilation. The tachyon total energy is (or reflects) 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 (chiral)
Superstring model | Invariant |
---|---|
Heterotic | |
IIA | |
IIB |
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
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,
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 correspondence
- dS/CFT correspondence
- Grand unification theory
- List of string theory topics
- String field theory
References
- ^ Polchinski, Joseph. String Theory: Volume I. Cambridge University Press, p. 4.
- ISBN 978-3-642-45128-7
- .
- S2CID 52026092.
- ^ Woit, Peter (February 22, 2011). "Implications of Initial LHC Searches for Supersymmetry".
- S2CID 53467362.
- ^ Falkowski, Adam (Jester) (February 16, 2011). "What LHC tells about SUSY". resonaances.blogspot.com. Archived from the original on March 22, 2014. Retrieved March 22, 2014.
- ^ Tapper, Alex (24 March 2010). "Early SUSY searches at the LHC" (PDF). Imperial College London.
- S2CID 22498269.
- .
- ^ from the original on March 22, 2014. Retrieved March 22, 2014.
- John H. Schwarzin Schwarz, J. H. (1972). "Physical states and pomeron poles in the dual pion model". Nuclear Physics, B46(1), 61–74.
- ^ Polchinski, Joseph. String Theory: Volume I. Cambridge University Press, p. 247.
- ^ Polchinski, Joseph. String Theory: Volume II. Cambridge University Press, p. 198.
- S2CID 120143992.
Cited sources
- Polchinski, Joseph (1998). String Theory Vol. 1: An Introduction to the Bosonic String. Cambridge University Press. ISBN 978-0-521-63303-1.
- Polchinski, Joseph (1998). String Theory Vol. 2: Superstring Theory and Beyond. Cambridge University Press. ISBN 978-0-521-63304-8.