  In this paper we study a hierarchical supersymmetric model for a class of
gapless, three-dimensional, weakly disordered quantum systems, displaying
pointlike Fermi surface and conical intersections of the energy bands in the
absence of disorder. We use rigorous renormalization group methods and
supersymmetry to compute the correlation functions of the system. We prove
algebraic decay of the two-point correlation function, compatible with
delocalization. A main technical ingredient is the multiscale analysis of
massless bosonic Gaussian integrations with purely imaginary covariances,
performed via iterative stationary phase expansions.
