Parisi-Sourlas mechanism and dimensional reduction in the bosonic string

The light-cone gauge path-integral is obtained from the conformal gauge fixed expression of Polyakov's theory for the bosonic string by integrating out the unphysical degrees of freedom. A generalized Parisi-Sourlas mechanism is shown to be responsible for the factorization of the integrations over the unphysical modes (and hence the dimensional reduction of the bosonic string) in the functional formulation of the theory. The corresponding decoupling mechanism in the canonical formulation of the theory is demonstrated to be the Kugo-Ojima 'quartet' mechanism. The equivalence of the Parisi-Sourlas mechanism in the functional approach with the Kugo-Ojima 'quartet' mechanism in the operator language is emphasized. (orig.)