Since the supersymmetry (SUSY) generators form together with the Poincaré algebra and superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way.
The minimal version of 4-dimensional supergravity (with unbroken local supersymmetry) was constructed in detail in 1976 by Dan Freedman, Sergio Ferrara and Peter van Nieuwenhuizen.
[6] The key issue of whether or not the spin 3/2 field is consistently coupled was resolved in the nearly simultaneous paper, by Deser and Zumino,[7] which independently proposed the minimal 4-dimensional model.
It was quickly generalized to many different theories in various numbers of dimensions and involving additional (N) supersymmetries.
The construction of a realistic model of particle interactions within the N = 1 supergravity framework where supersymmetry (SUSY) breaks by a super Higgs mechanism carried out by Ali Chamseddine, Richard Arnowitt and Pran Nath in 1982.
Collectively now known as minimal supergravity Grand Unification Theories (mSUGRA GUT), gravity mediates the breaking of SUSY through the existence of a hidden sector.
mSUGRA naturally generates the Soft SUSY breaking terms which are a consequence of the Super Higgs effect.
Radiative breaking of electroweak symmetry through Renormalization Group Equations (RGEs) follows as an immediate consequence.
Due to its predictive power, requiring only four input parameters and a sign to determine the low energy phenomenology from the scale of Grand Unification, its interest is a widely investigated model of particle physics One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the theory of everything.
Many of the details of the theory were fleshed out by Peter van Nieuwenhuizen, Sergio Ferrara and Daniel Z. Freedman.
Problems included:[citation needed] Some of these difficulties could be avoided by moving to a 10-dimensional theory involving superstrings.
[12] The core breakthrough for the 10-dimensional theory, known as the first superstring revolution, was a demonstration by Michael B.
Today we know that, using D-branes for example, gauge symmetries can be introduced in other 10-dimensional theories as well.
There were too many Calabi–Yaus to compactify on, many more than Yau had estimated, as he admitted in December 2005 at the 23rd International Solvay Conference in Physics.
Joseph Polchinski realized that obscure string theory objects, called D-branes, which he discovered six years earlier, equate to stringy versions of the p-branes known in supergravity theories.
Thanks to supersymmetry, p-branes in supergravity gained understanding well beyond the limits of string theory.
Furthermore, he argued that M-theory's long wavelength limit, i.e. when the quantum wavelength associated to objects in the theory appear much larger than the size of the 11th dimension, needs 11-dimensional supergravity descriptors that fell out of favor with the first superstring revolution 10 years earlier, accompanied by the 2- and 5-branes.
Therefore, supergravity comes full circle and uses a common framework in understanding features of string theories, M-theory, and their compactifications to lower spacetime dimensions.
The term "low energy limits" labels some 10-dimensional supergravity theories.
Due to string dualities, the conjectured 11-dimensional M-theory is required to have 11-dimensional supergravity as a "low energy limit".
Before we move on to SUGRA proper, let's recapitulate some important details about general relativity.
The supervierbein and spin connection are real in the sense that they satisfy the reality conditions The covariant derivative is defined as The covariant exterior derivative as defined over supermanifolds needs to be super graded.
This means that every time we interchange two fermionic indices, we pick up a +1 sign factor, instead of -1.
for some coefficients c. Unlike nonSUSY GR, the torsion has to be nonzero, at least with respect to the fermionic directions.
is a shorthand notation to mean the index runs over either the left or right Weyl spinors.
The action for a SUGRA theory with chiral superfields X, is given by where K is the Kähler potential and W is the superpotential, and
Unlike the case for flat superspace, adding a constant to either the Kähler or superpotential is now physical.
It can be found from a dimensional reduction of 11D supergravity by making the size of 7 of the dimensions go to zero.
Thus the limit on the number of supercharges cannot be satisfied in a spacetime of arbitrary dimension.
Some theoretical examples in which this is satisfied are: The supergravity theories that have attracted the most interest contain no spins higher than two.