Redirected from M Theory
The following article is somewhat technical in nature, see Mtheory simplified for a less technical article.
Mtheory's relation to superstrings and supergravity
MTheory 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 duality. Two physical theories are dual to each other if they have identical physics after a certain mathematical transformation.
Type IIA and IIB are related by Tduality[?], as are the two Heterotic theories. Type I and Heterotic SO(32) are related by the Sduality[?]. Type IIB is also Sdual with itself.
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 elevendimensional spacetime display two tendimensional boundaries. The strong coupling limit of either theory produces an 11dimensional spacetime. This elevendimensional description of the underlying theory is called "M theory". A string's spacetime history can be viewed mathematically by functions like
that describe how the string's twodimensional sheet coordinates (σ,τ) map into spacetime X^{μ}
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 contant and the traditional perturbative string theory presumes it to be infinitesimal. Another interpretation is that dimension is not a fundamental concept of Mtheory at all.
Mtheory contains much more than just strings. It contains both higher and lower dimensional objects. These objects are called pbranes where p denotes their dimensionality (thus, 1brane for a string and 2brane for a membrane). Higher dimensional objects were always present in superstring theory but could never be studied before the Second Superstring Revolution because of their nonperturbative[?] nature.
Insights into nonperturbative properties of pbranes stem from a special class of pbranes called Dirichlet pbranes (Dpbranes). This name results from the boundary conditions assigned to the ends of open strings in type I superstrings.
Open strings of the type I theory can have endpoints which satisfy the Neumann boundary condition. Under this condition, the endpoints of strings are free to move about but no momentum can flow into or out of the end of a string. The T duality infers the existence of open strings with positions fixed in the dimensions that are Ttransformed. Generally, in type II theories, we can imagine open strings with specific positions for the endpoints in some of the dimensions. This lends an inference that they must end on a preferred surface. Superficially, this notion seems to break the relativistic invariance of the theory, possibly paradoxical. The resolution of this paradox is that strings end on a pdimensional dynamic object, the Dpbrane.
The importance of Dbranes stems from the fact that they make it possible to study the excitations of the brane using the renormalizable 2D quantum field theory of the open string instead of the nonrenormalizable worldvolume theory of the Dbrane itself. In this way it becomes possible to compute nonperturbative phenomena using perturbative methods. Many of the previously identified pbranes are Dbranes ! Others are related to Dbranes by duality symmetries, so that they can also be brought under mathematical control. Dbranes have found many useful applications, the most remarkable being the study of black holes. Strominger and Vafa have shown that Dbrane techniques can be used to count the quantum microstates associated to classical black hole configurations. The simplest case first explored was static extremal charged black holes in five dimensions. Strominger and Vafa proved for large values of the charges the entropy S = log N, where N is equal to the number of quantum states that system can be in, agrees with the BekensteinHawking[?] prediction (1/4 the area of the event horizon).
This result has been generalized to black holes in 4D as well as to ones that are near extremal (and radiate correctly) or rotating, a remarkable advance. It has not yet been proven that there is any problematic breakdown of quantum mechanics due to black holes.
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