  Focusing on multifractal properties we investigate electric transport on
random resistor diode networks at the phase transition between the
non-percolating and the directed percolating phase. Building on first
principles such as symmetries and relevance we derive a field theoretic
Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of
the current distribution that are governed by a family of critical exponents
$\{\psi_l \}$. We calculate the family $\{\psi_l \}$ to two-loop order in a
diagrammatic perturbation calculation augmented by renormalization group
methods.
