In four spacetime dimensions, N=8 Supergravity is the most symmetricquantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of 11D supergravity by making the size of seven of the dimensions go to zero. It has eight supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin -2. More supersymmetries would mean the particles would have superpartners with spins higher than 2. The only theories with spins higher than 2 which are consistent involve an infinite number of particles. Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything. However, in later years this was abandoned in favour of String Theory. There has been renewed interest in the 21st century, with the possibility that this theory may be finite.
Calculations
It has been found recently that the expansion of N=8 Supergravity in terms of Feynman diagrams has shown that N=8 Supergravity is in some ways a product of two N = 4 super Yang–Mills theories. This is written schematically as: N = 8 Supergravity = × This is not surprising, as N=8 supergravity contains six independent representations of N=4 Super Yang–Mills.
Particle content
The theory contains 1 graviton, 8 gravitinos, 28 vector bosons, 56 fermions, 70 scalar fields where we don't distinguish particles with negative spin. These numbers are simple combinatorial numbers that come fromPascal's Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes. One reason why the theory was abandoned was that the 28 vector bosons which form an O gauge group is too small to containthe standard model UxSUxSU gauge group, which can only fit within the orthogonal group O. For model building, it has been assumed that almost all the supersymmetries would be broken in nature, leaving just one supersymmetry, although nowadays because of the lack of evidence for N=1 supersymmetry higher supersymmetries are now being considered such as N=2.
N=8 Supergravity can be viewed as the low energy approximation of the type IIA or type IIB superstring with 6 of its dimensions compactified on a 6-torus. Equivalently, it may also be viewed as 11D M-Theory with seven of its dimensions compactified on a 7-torus.
Global symmetries
Some surprising global symmetries have been found in this theory. For example, it has been shown that there is an E₇global symmetry but in order for the theory to be finite it is thought that there may be other symmetries not yet found.
