International audienceIn this paper we create a complete gravity torque map of the disk of the LINER/Seyfert 1.9 galaxy NGC 4579. We quantify the efficiency of angular momentum transport and search for signatures of secular evolution in the fueling process from r ~ 15 kpc down to the inner r ~ 50 pc around the active galactic nucleus (AGN). We use both the 1-0 and 2-1 line maps of 12CO obtained with the Plateau de Bure Interferometer (PdBI) as part of the NUclei of Galaxies-(NUGA)-project. The CO(1-0) and CO(2-1) PdBI maps at 2.0 arcsec × 1.3 arcsec and 1.0 arcsec × 0.6 arcsec resolution, respectively, include the short spacing correction provided by IRAM-30 m data. We derive the stellar potential from an NIR (K band) wide field image of th...