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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, D-branes are seen as compactified membranes from 11D M-theory.
In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments. [21]
It was also realized by Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten in 1985 that to obtain = supersymmetry, the six small extra dimensions (the D = 10 critical dimension of superstring theory had been originally discovered by John H. Schwarz in 1972) [48] need to be compactified on a Calabi–Yau manifold. [49]
The core breakthrough for the 10-dimensional theory, known as the first superstring revolution, was a demonstration by Michael B. Green, John H. Schwarz and David Gross that there are only three supergravity models in 10 dimensions which have gauge symmetries and in which all of the gauge and gravitational anomalies cancel.
Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have N = 2 {\displaystyle {\mathcal {N}}=2} extended supersymmetry which is maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions.
At low energies, type I string theory is described by the type I supergravity in ten dimensions coupled to the SO(32) supersymmetric Yang–Mills theory. The discovery in 1984 by Michael Green and John H. Schwarz that anomalies in type I string theory cancel sparked the first superstring revolution. However, a key property of these models ...
F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus.By doing so, one obtains type IIB superstring theory in 10 dimensions.
These bosonic fields have a physical interpretation as the coordinates of the string worldsheet embedded in spacetime, with running over the number of spacetime dimensions. For superstring theory in flat spacetime consistency of the theory requires exactly ten dimensions.