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Conserved directed-percolation (C-DP) and the depinning transition of adisordered elastic interface belong to the same universality class as has beenproven very recently by Le Doussal and Wiese [Phys. Rev. Lett.~\textbf{114},110601 (2015)] through a mapping of the field theory for C-DP onto that of thequenched Edwards-Wilkinson model. Here, we present an alternative derivation ofthe C-DP field theoretic functional, starting with the coherent state pathintegral formulation of the C-DP and then applying theGrassberger-transformation, that avoids the disadvantages of the so-calledDoi-shift. We revisit the aforementioned mapping with focus on a specific termin the field theoretic functional that has been problematic in the past when itcame to assessing its relevance. We show that this term is redundant in thesense of the renormalization group.

Directed Percolation with a Conserved Field and the Depinning Transition