S-duality (string theory)
In addition to the T-duality in string theory , the S-duality is a derivation of the M-theory , which tries to unite the five superstring theories. Most superstring theories show dualities with one another, which is why they were summarized in 1995 by the mathematician Edward Witten to form the M-theory, which is still not properly understood.
The fault calculation
In order to be able to understand the S-duality, the concept of the string coupling constant must be introduced. Due to the complexity of the string equations, approximations are used which, although they represent a considerable relief, are only an approximation to the exact equations. The so-called disturbance calculation is used here. Strings interact with each other by merging and splitting. If the quantum fluctuations, according to which virtual string-anti-string pairs arise spontaneously, are included in the equation of motion, then they have an enormous influence on the movements and interactions of the string.
Similar to elementary particle physics, which works with Feynman diagrams, there are also diagrams in string theory in which the world surfaces of the strings (and, accordingly, their interactions) can be represented, the so-called loop diagrams.
Since an infinite number of particle-antiparticle pairs can arise in quantum mechanics, one would have to add an infinite number of interaction processes to this loop diagram. The perturbation calculation is based on a homogeneous space in which no quantum fluctuations take place, which is then an approximation. This is called a zero loop diagram.
The string coupling constant
In the usual elementary particle physics, it is mainly calculated with coupling constants that define the strength of the given force. In string theory, however, it is the probability with which a string splits up into a virtual string-anti-string pair. If the value is less than 1, the fewer loops there are in the diagram, the higher the probability. If the value is greater than 1, then it is exactly the opposite. So the zero loop process is a very good approximation of the actual interaction. One of the biggest problems in string theory is the determination of the exact coupling constant, as it has a considerable influence on the perturbation calculation, the masses and the energies of the strings. In most cases it is only possible to make statements about a universe based on strings if one starts from the case of coupling constant ≤ 1. However, it could be shown that under certain conditions, with coupling> 1, particles with certain states can be determined. Under these circumstances one can see that it is much easier to describe a universe based on weak coupling. Edward Witten was able to show in 1995 that the physical properties of the string theory of type I with strong coupling and O-heterotic with weak coupling are the same. This duality as well as the T-duality occur in almost all superstring theories.
Derivation to the M-theory
The fact that two (super) string theories can possibly be T-dual or S-dual to one another led Witten to assume in 1995 that all string theories as well as supergravity are only part of a larger, more comprehensive theory that he then tried to develop . He also discovered that when the coupling constant of an (e-heterotic) string is increased, it becomes a 2-manifold, a membrane.
The theory that describes these facts is the M-theory, which, however, has not yet been fully understood.
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- Wikibooks: The String Theory - A Popular Science Introduction - Learning and Teaching Materials
