Casella di testo: Supergravity

 Supergravity is the gauge theory of supersymmetry, that is it
 describes systems which are left invariant by the action of  space-time dependent  (local) supersymmetry transformations. 
Supersymmetry is a symmetry between bosons (integer spin particles)  and fermions (half-integer spin particles). The consecutive action of two supersymmetry transfromations produces a translation. This property is represented by the following relation between the infinitesimal generators of  supersymmetry  Q, and the infinitesimal generator of space-time translations (the momentum 4-vector p): 


As a consequence of this, invariance under local supersymmetry transformations  implies invariance under general coordinate transformations, which is the basic assumption of Einsteinís theory of Gravitation.  Supergravity therefore comprises in a natural way General Relativity.

Supergravity from Superstring Theory 

Superstring theory is a very promising candidate for a quantum theory in which gravity is naturally unified with the other fundamental interactions. Like more standard field theories, superstring theory is defined perturbatively in its coupling constant. In this case however the coupling constant is not a parameter of the theory, but is a dynamical quantity defined as the vacuum expectation value of a suitable scalar field. If our universe is realized in a suitable vacuum of this theory, non-perturbative objects will play a crucial role in determining the symmetry properties of such a state (as it happens for QCD). A dynamical mechanism  accounting for the choice of this vacuum requires a deeper understanding of the non-perturbative structure of the theory. A valuable framework for studying the low-energy string dynamics around non-perturbative vacua in limits in which a consistent formulation  of the string theory is missing, has often been provided by supergravity. This field theory  describes the infinite tension (low-energy) limit of superstring theory  and, as mentioned above,  naturally encodes Einsteinís General Relativity  as a consequence of its local supersymmetry .
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