11-dimensional Supergravity

Supergravity - 1970s

Supergravity is restrictive, as it places an upper limit on the number of dimensions that it can be consistently formulated in: 11 (as opposed to general relativity, which can be formulated in any arbitrary number of dimensions, though it is often formulated in 4, to match our physical world). This is the simplest way to include matter in a consistent theory of supergravity: formulate it in 11 dimensions. 

1978: Werner Nahm

Showed that 11, was the maximum number of dimensions that a consistent theory of supersymmetry can be formulated in. This is despite the fact that when supergravity was initially formulated at Stony Brook, it was formulated in 4 dimensions.

1978: Joel Scherk, Bernard Julia and Eugene Cremmer

Showed that supergravity, is most elegant, with 11 as the maximum number of dimensions. This allowed for local supersymmetry and for no fields with spin higher than 2.

There was hope that by constructing various compactifications (a method that makes extra dimensions curled up and small enough to be undetectable) of supergravity in 11 dimensions, a unified theory of nature’s fundamental forces could be constructed: gravity, electromagnetism, and the strong and weak nuclear forces.

The decline of supergravity:

However, there were problems with 11-dimensional supergravity:

• It could not provide an explanation for a phenomenon in the Standard Model, known as chirality, where the laws of physics distinguish between clockwise and counterclockwise.

• It did not provide a consistent theoretical picture of gravity and quantum mechanics. The theory had problems with uniting the forces of nature. The theory was too small to account for all classes of subatomic particles.

It became clear that supergravity could not be quantized correctly. Supergravity failed because, whenever physicists tried to calculate numbers in this theory, they would arrive at meaningless infinities. The theory had fewer infinities than the Kaluza-Klein theory, however, it was still not renormalizable. Another problem was that the largest symmetry that supergravity could include was called O(8) and it was still too small to contain all of the symmetry of the Standard Model.