  Disordered noninteracting quasiparticles that are governed by a Majorana-type
Hamiltonian -- prominent examples are dirty superconductors with broken
time-reversal and spin-rotation symmetry, or the fermionic representation of
the 2d Ising model with fluctuating bond strengths -- are called class D. In
two dimensions, weakly disordered systems of this kind may possess a metallic
phase beyond the insulating phases expected for strong disorder. We show that
the 2d metal phase emanates from the free Majorana fermion point, in the
direction of the RG trajectory of a perturbed WZW model. To establish this
result, we develop a supersymmetric extension of the method of nonabelian
bosonization. On the metallic side of the metal-insulator transition, the
density of states becomes nonvanishing at zero energy, by a mechanism akin to
dynamical mass generation. This feature is explored in a model of N species of
disordered Dirac fermions, via the mapping on a nonlinear sigma model, which
encapsulates a Z_2 spin degree of freedom. We compute the density of states in
a finite system, and obtain agreement with the random-matrix prediction for
class D, in the ergodic limit. Vortex disorder, which is a relevant
perturbation at the free-fermion point, changes the density of states at low
energy and suppresses the local Z_2 degree of freedom, thereby leading to a
different symmetry class, BD.
