/ 92 04 06 1 v 1 2 0 A pr 1 99 2 CNLS - 92 - 02 March 1992 MARINARI - PARISI AND \ SUPERSYMMETRIC COLLECTIVE FIELD THEORY

A field theoretic formulation of the Marinari-Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersym-metrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari-Parisi models a continuum limit similar to that of the d = 1 bosonic string.