  We find an analog of Zamolodchikov's c-theorem for disordered two dimensional
noninteracting systems in their supersymmetric representation. For this purpose
we introduce a new parameter b which flows along the renormalization group
trajectories much like the central charge for unitary two dimensional field
theories. However, it is not known yet if this flow is irreversible. b turns
out to be related to the central extension of a certain algebra, a
generalization of the Virasoro algebra, which we show may be present at the
critical points of these theories. b is also related to the physical free
energy of the disordered system defined on a cylinder. We discuss possible
applications by computing b for two dimensional Dirac fermions with random
gauge potential.
