Supergravity Theory
Supergravity theories merge the notions of supersymmetry and gravitation. Supersymmetry requires that every bosonic particle (integer spin) has a fermionic counterpart (half-integer spin) and vice versa. Spin-0 particles (scalars) and spin-1 particles (vectors), together with their identical mass spin-½ superpartners, comprise supermultiplets. It is natural to ask whether a gauge transformation can mediate a change from a bosnic degree of freedom to a fermionic one. Such an operation is highly non-trivial. Since spin has units of angular momentum, changing the spin of a particle also alters its space-time coordinates. In contrast, a gauge transformation within the context of the standard model rephases a field, and this effect is compensated by a shift of the covariant derivative in such a way that the Lagrangian of the theory remains invariant. The key difference here is that the position of the field itself is unchanged.
The general theory of relativity treats the gravitational force in terms of the response of matter to the curvature of space-time, which in turn results from the presence of matter or energy.
A gauge transformation in the theory of gravity can therefore be thought of as producing a slight displacement in the position of a particle. A theory that allows transitions among particles of different spin must also be consistent with the theory of gravity. In particular, it must include a particle that mediates gravity as a fundamental force on an equal footing with the electromagnetic, strong, and weak interactions. That particle is the graviton, and it carries spin-2. The supersymmetric partner of the graviton is called a gravitino, and it has spin-3/2.
Different supergravity theories are classified by the types of particles in each supermultiplet. The extensively studied N=8 theory, has supermultiplets with particles of all spins between 0 and 2. Because supergravity treats each of the fundamental forces in a similar way, it was initially viewed as a candidate for the so-called theory of everything, which would unify all of physics. Unfortunately, infinities in the theory do not completely cancel because gravity is not renormalizable. However, because supersymmetry and supergravity can be extended to a theory with more than four space-time dimensions, these concepts served as an important step towards constructing superstring theory.
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