N=8 Supergravity

N=8 Supergravity is the most symmetric quantum 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 7 of the dimensions go to zero. It has 8 supersymmetries which is the most any gravitational theory can have since there are 8 half-steps between spin 2 and spin -2. (The spin 2 graviton is the particle with the highest spin in this theory). 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 (such as String Theory and Higher-Spin Theories). 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 = (N = 4 Super Yang–Mills) × (N = 4 Super Yang–Mills)

This is not so surprising as N=8 supergravity contains 6 independent representations of N=4 Super Yang–Mills.

Particle content

The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don't distinguish particles with negative spin. These numbers are simple combinatorial numbers that come from Pascal's Triangle.

One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1)xSU(2)xSU(3) gauge group which can only fit within the orthogonal group O(10).

For model building, it has been assumed that almost all the supersymmetries would be broken in nature leaving just 1 supersymmetry (N=1) although nowadays because of the lack of evidence for N=1 supersymmetry higher supersymmetries are now being considered such as N=2.

Connection with superstring theory

N=8 Supergravity can be viewed as the low energy approximation of 11D M-Theory with 7 of its dimensions on a certain compact surface.

Extensions

When derived from Heterotic Superstring Theory compactified on higher-dimensional tori, there are two extensions to N=8 Supergravity. They are the coupling of additional fields which form E₈xE₈ N=4 Super-Yang Mills and SO(32) N=4 Super Yang–Mills. When adding those fields the number of particles increases to 256 + 496x16 = 8192 = 2¹³ particles.

Global symmetries

Some surprising global symmetries have been found in this theory. For example, it has been shown that there is an E₇ global symmetry but in order for the theory to be finite it is thought that there may be other symmetries not yet found.