M-theory

M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. According to Dr. Edward Witten, who proposed the theory, mathematical tools which have yet to be invented are needed in order to fully understand it.

M-theory's relation to superstrings and supergravity

M-Theory in various geometric backgrounds is associated with the different superstring theories (in different geometric backgrounds), and these limits are related to each other by the principle of dualism. Two physical theories are dual to each other if they have identical physics after a certain mathematical transformation.

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Type IIA and IIB are related by T-duality, as are the two Heterotic theories. Type I and Heterotic SO(32) are related by the S-duality. Type IIB is also S-dual with itself.

Related Topics:
Type IIA - IIB - T-duality - Heterotic - Type I - SO(32) - S-duality

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• The type II theories have two supersymmetries in the ten-dimensional sense, the rest just one.
• The type I theory is special in that it is based on unoriented open and closed strings.
• The other four are based on oriented closed strings.
• The IIA theory is special because it is non-chiral (parity conserving).
• The other four are chiral (parity violating).

In each of these cases there is an 11th dimension that becomes large at strong coupling. In the IIA case the 11th dimension is a circle. In the HE case it is a line interval, which makes eleven-dimensional space-time display two ten-dimensional boundaries. The strong coupling limit of either theory produces an 11-dimensional space-time. This eleven-dimensional description of the underlying theory is called "M- theory". A string's space-time history can be viewed mathematically by functions like

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:X^mu(sigma, au)

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that describe how the string's two-dimensional sheet coordinates (sigma, au) map into space-time X^mu.

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One interpretation of this result is that the 11th dimension was always present but invisible because the radius of the 11th dimension is proportional to the string coupling constant and the traditional perturbative string theory presumes it to be infinitesimal. Another interpretation is that dimension is not a fundamental concept of M-theory at all.

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