Extended Supersymmetry and Extended Supergravity Theories

Abstract

The failure of quantized gravity in interaction with quantized matter fields (whether scalar, spinor of vector fields) to provide renormalizable results even at the one loop level [1] has led to a situation analoguous to the puzzle of the V-A theory of weak interactions before the advent of gauge theories. The V-A theory of weak interactions was known to be correct at the tree approximation, but having a coupling constant whose dimension was the inverse of a mass squared (G_F = 1. 01 10⁻⁵GeV⁻²) it was giving divergent and non renormalizable answers even at the one loop level. In a similar fashion, classical general relativity is known to describe gravity accurately, but quantum gravity leads to divergent results, except in the one loop case and for pure gravity [l]. The analogy with the V-A theory of weak interactions is even stronger if one remarks that the coupling constant of gravity also has the dimension of the inverse of a mass $\left( {K \sim \,\left( {{G_N}} \right)\frac{1}{2}\, \sim \,.8\,{{10}^{ - 19}}\,Ge{V^{ - 1}}} \right)$. One can think that the trouble with quantized gravity is due to the perturbative approach rather than with the theory itself. The other possibility is to look for alternative theories of gravity which would be free of divergences.