M theory

The five string theories and 11-dimensional supergravity as borderline cases of the M-theory.

The M-theory is an attempt to expand and generalize string theory in theoretical physics . This theory is an area of ​​intensive research, since it is hoped that it will be able to describe all known natural forces in a uniform manner .

Details

The M-Theory was born during the so-called second superstring revolution, with major contributions from Edward Witten , who gave a widely acclaimed lecture on it at a conference at the University of Southern California in 1995 . The five well-known superstring theories ( Type I , Type IIA and IIB as well as the two heterotic string theories , labeled E8 and SO (32) in the picture) and the eleven-dimensional supergravity are considered as borderline cases of a more fundamental theory.

The connections between the different theories are given by dualities , such as S-duality and T-duality . With their help one can show that the different theories calculate the same results, but in different areas of their parameter space. This makes it possible to make statements about the underlying theory in different border areas, although an explicit formulation is not known.

The eleven-dimensional supergravity occupies a special position in a certain way, since it has the maximum number of dimensions for a supergravity theory, in contrast to the string theories, which are formulated in ten dimensions. Eleven-dimensional supergravity is also a classical (i.e. non- quantized ) theory, whereas the string theories are quantum theories . The connection of supergravity with the heterotic E8 × E8 string theory or Type IIA is achieved by compacting the eleventh dimension on an interval (marked with in the figure ) or on a circle ( ). In addition, one considers the supergravity limit of the theory on the string side . ${\displaystyle I}$ ${\displaystyle S^{1}}$

Non- perturbative statements about the M-theory can be made with the help of D-branes or M-branes. However, there is currently no complete, non-perturbative formulation of the M-theory, which is also due to the fact that no conformal field theory can be constructed for more-than-one-dimensional objects (see Polyakov effect ).

Naming

The meaning given for the letter M in the designation of the theory is not uniform. Edward Witten proposed the term in 1995 with reference to the membrane structure of the theory. At the same time he himself was skeptical as to whether the still young theory would actually amount to one and remarked early on, rather jokingly, that the 'M' could "optionally stand for magical, enigmatic (original: mystery) or membrane ". Other candidates named were Matrix (after a suggestion for M-Theory by Tom Banks and others), mother of all string theories and it was even suspected that it stood for an upside-down “W” as a synonym for “Witten” or that the letter "M" as the only letter next to the "W" connects five points harmoniously, whereby the five points stand for the five previously contradicting string theories. In an interview published in 2013, he made it clear: “Some colleagues thought there was an eleven-dimensional theory based on membranes. But I wasn't convinced that it would work completely. But I also didn't know if she was wrong, and I didn't want to contradict her. So I kept the M from “membrane” and said that with time it would become clear whether the M stands for “magic”, “mystery” or “membrane”. Later, the membranes were derived from matrices, and by chance the matrix theory also starts with "M". "

Possible representations

In late 1996, Tom Banks , Willy Fischler , Stephen Shenker and Leonard Susskind proposed the BFSS matrix model as a possible representation of the M-theory . They pointed out that the limit of a supersymmetric matrix theory is equivalent to the eleven-dimensional, uncompactified M-theory. The membranes of the M-theory are stimuli in the matrix theory, the world volume of the membranes having a non-commutative geometry that is embedded in a non-commutative space-time. ${\displaystyle N\to \infty }$

A simple case of the BFSS model is a 0 + 0 dimensional theory, the effect of which is written as a dimensional reduction of a 9 + 1 dimensional Super Yang Mills theory

${\displaystyle S=\operatorname {Tr} \left({\frac {1}{4}}[X_{\mu },X_{\nu }][X^{\mu },X^{\nu }]+\theta ^{T}\gamma _{0}\gamma _{\mu }[X^{\mu },\theta ]+\beta *1]\right),}$

where Hermitian N × N matrices are, SO (9) Pauli matrices in their representation in 16 dimensions and a spinor with spin (9,1) with 16 components. Roughly speaking, this effect describes a quantum mechanics with matrix degrees of freedom. ${\displaystyle X}$ ${\displaystyle \gamma }$ ${\displaystyle \theta }$

literature

• Michael J. Duff : The Theory formerly known as Strings , Scientific American, February 1998, pdf
• Edward Witten: Magic, Mystery and Matrix , Not. Amer. Math. Soc., Volume 45 , 1998, p. 1124, PDF file

Web links

Wiktionary: M-Theory  - explanations of meanings, word origins, synonyms, translations

• M-theory, the theory formerly known as Strings ( University of Cambridge )
• M-theory ( Caltech )
• The Elegant Universe with Brian Greene (English, popular science TV show on Nova based on the book of the same name, with transcript)

Individual evidence

1. ↑ John H. Schwarz: 'The Power of M Theory', Oct 1995. Footnote 2 (hep-th / 9510086), http://arxiv.org/pdf/hep-th/9510086v1.pdf
2. ↑ Edward Witten: 'Five-branes and M-Theory On An Orbifold', Jan 1996 (hep-th / 9512219), http://arxiv.org/pdf/hep-th/9512219v1.pdf
3. ↑ Michio Kaku Into the eleventh dimension , Online ( Memento from October 16, 2002 in the Internet Archive )
4. ↑ Interview with Rüdiger Vaas in Bild der Wissenschaft No. 5 (2013), p. 58.
5. ↑ M-theory as a matrix model: A conjecture, T. Banks, W. Fischler, SH Shenker, L. Susskind
6. ↑ Proposals on nonperturbative superstring interactions, Lubos Motl