It contains a graviton, a gravitino, and a 3-form gauge field, with their interactions uniquely fixed by supersymmetry.
Discovered in 1978 by Eugène Cremmer, Bernard Julia, and Joël Scherk, it quickly became a popular candidate for a theory of everything during the 1980s.
[1] However, interest in it soon faded due to numerous difficulties that arise when trying to construct physically realistic models.
It came back to prominence in the mid-1990s when it was found to be the low energy limit of M-theory, making it crucial for understanding various aspects of string theory.
supergravity since this was an attractive candidate for a theory of everything, stemming from the fact that it unifies particles of all physically admissible spins into a single multiplet.
Werner Nahm showed in 1978 that supersymmetry with spin less than or equal to two is only possible in eleven dimensions or lower.
[2] Motivated by this, eleven-dimensional supergravity was constructed by Eugène Cremmer, Bernard Julia, and Joël Scherk later the same year,[1] with the aim of dimensionally reducing it to four dimensions to acquire the
This began in 1980 when Peter Freund and Mark Ruben showed that supergravity compactifies preferentially to four or seven dimensions when using a background where the field strength tensor is turned on.
[4] Additionally, Edward Witten argued in 1981 that eleven dimensions are also the minimum number of dimensions needed to acquire the Standard Model gauge group, assuming that this arises as subgroup of the isometry group of the compact manifold.
[5][nb 1] The main area of study was understanding how 11D supergravity compactifies down to four dimensions.
However, a number of problems were quickly identified with these approaches which eventually caused the program to be abandoned.
[7] One of the main issues was that many of the well-motivated manifolds could not yield the Standard Model gauge group.
Additionally, these compactifications generally yielded very large negative cosmological constants which could be hard to remove.
[nb 3] Lastly, quantizing the theory gave rise to quantum anomalies which were difficult to eliminate.
Due to these issues, 11D supergravity was abandoned in the late 1980s, although it remained an intriguing theory.
Indeed, in 1988 Michael Green, John Schwartz, and Edward Witten wrote of it that[9] It is hard to believe that its existence is just an accident, but it is difficult at the present time to state a compelling conjecture for what its role may be in the scheme of things.In 1995, Edward Witten discovered M-theory,[10] whose low-energy limit is 11D supergravity, bringing the theory back into the forefront of physics and giving it an important place in string theory.
In supersymmetry, the maximum number of real supercharges that give supermultiplets containing particles of spin less than or equal to two, is 32.
[11]: 265 Supercharges with more components result in supermultiplets that necessarily include higher spin states, making such theories unphysical.
It has a single multiplet consisting of the graviton, a Majorana gravitino, and a 3-form gauge field.
All hatted variables are supercovariant in the sense that they do not depend on the derivative of the supersymmetry parameter
M2-branes and M5-branes have a regular non-degenerate event horizon whose constant time cross-sections are topologically 7-spheres and 4-spheres, respectively.
The Freund–Rubin compactification of 11D supergravity shows that it preferentially compactifies to seven and four dimensions, which led to it being extensively studied throughout the 1980s.
One additionally demands that the solution is stable against fluctuations, which in anti-de Sitter spacetimes requires that the Bretenlohner–Freedman bound is satisfied.
A similar widely studied compactification was using a squashed 7-sphere, which can be acquired by embedding the 7-sphere in a quaternionic projective space, with this giving a gauge group of
A key property of 7-sphere Kaluza-Klein compactifications is that their truncation is consistent, which is not necessarily the case for other Einstein manifolds besides the 7-torus.
Physically this needs not be a problem in compactifications to Minkowski spacetimes as the inconsistent truncation merely results in additional irrelevant operators in the action.
However, most Einstein manifold compactifications are to anti-de Sitter spacetimes which have a relatively large cosmological constant.
[15] This is not a proper eleven-dimensional theory since the fields explicitly do not depend on one of the coordinates, but it is nonetheless useful for studying massive branes.
[16] While eleven-dimensional supergravity is not UV finite, it is the low energy limit of M-theory.
[8]: 469–471 Unlike for supergravity in other dimensions, an extension to eleven dimensional anti-de Sitter spacetime does not exist.