Marinari-Parisi and Supersymmetric Collective Field Theory

TL;DR

This paper develops a field theoretic formulation of the Marinari-Parisi supersymmetric matrix model, connecting it to supersymmetric collective string field theory and super-Calogero models, and analyzes its perturbation theory and spectrum.

Contribution

It establishes a new field theoretic framework for the Marinari-Parisi model, linking it to supersymmetric string field theory and super-Calogero models, and explores its perturbative vertices and spectral properties.

Findings

Equivalent to a supersymmetric collective string field theory

Identifies potentials with massless boson and Majorana fermion spectrum

Shows limitations in generating a continuum limit similar to d=1 bosonic string

Abstract

A field theoretic formulation of the Marinari-Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization 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.