Intrinsic Geometry of Supergravity

Abstract

Supersymmetry and supergravity provide a considerable extension of possibilities and a new understanding of the unification tendency. It is appropriate to recall here the early attempts of Feza Gürsey and others [1,2] in the sixties to unify the spacetime symmetries with the internal ones. Due to the analysis of these attempts there appear important no-go theorems concerning impossibility of such a merging in the framework of standard groups. At the same time internal symmetry can be nontrivially merged with the space-time one in the framework of supergroups, i. e., in supersymmetric models. After a remarkable success of the unified electroweak theory public opinion has been consolidated that this theory together with quantum chromodynamics will amalgamate into some gauge theory of grand unification of weak electromagnetic and strong interactions. In such a theory all the interacting fields (photon, intermediate bosons, gluons, etc.) come out on at least formally equal footings as gauge fields. At this stage there remains still an essential difference between them and the matter fields of leptons and quarks. The introduction of supersymmetry can help to eliminate this difference. Both the fermionic and bosonic fields can be equally the gauge ones in supersymmetric theories. These fields are functions of coordinates. One can try to eliminate this last difference and to equate in rights fields with coordinates. It is conceivable that supergravity will be useful to this end. In any case supergravity makes the next step and it has a claim to unify all the basic interactions including gravitation.