N=1 supergravity as a nonlinear realization.

Abstract

The $N=1$ supergravity in superspace (more precisely the minimal Einstein version of it) is consistently reformulated as a simultaneous nonlinear realization of two complex finite-dimensional supergroups generating via their closure the whole infinite-dimensional $N=1$ supergravity group and having in their intersection the rigid $N=1$ Poincar\'e supergroup chosen as the vacuum-stability subgroup. Thus $N=1$ supergravity is found to be a kind of nonlinear \ensuremath{\sigma} model describing a partial spontaneous breaking of the infinite-dimensional supersymmetry down to the rigid $N=1$ supersymmetry. The only independent Goldstone superfield accompanying this breaking appears to be an axial-vector superfield ${H}^{\ensuremath{\mu}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\mu}}}(x,\ensuremath{\theta},\overline{\ensuremath{\theta}})$ identified with the $N=1$ supergravity prepotential. All the other Goldstone superfields are expressed in terms of ${H}^{\ensuremath{\mu}\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\mu}}}$ by imposing appropriate covariant constraints on the corresponding Cartan superforms (the inverse Higgs effect). Thereby, the 15-year-old result of Borisov and Ogievetsky who interpreted Einstein gravity as a nonlinear $\ensuremath{\sigma}$ model is generalized to the $N=1$ supergravity case. Possible implications of the proposed formulation are discussed. In particular, the intriguing analogy between $N=1$ supergravity and the (super) $p$-brane theories is pointed out.