Spatially resolving the inner dust cavity of the transitional disks is a key to understanding the connection between planetary formation and disk dispersal. The disk around the Herbig star HD 139614 is of particular interest since it presents a pretransitional nature with an au-sized gap, in the dust, that was spatially resolved by mid-IR interferometry. Using new NIR interferometric observations, we aim to characterize the 0.1-10~au region of the HD~139614 disk further and identify viable mechanisms for the inner disk clearing. We report the first multiwavelength radiative transfer modeling of the interferometric data acquired on HD~139614 with PIONIER, AMBER, and MIDI, complemented by Herschel/PACS photometries. We confirm a gap structure in the um-sized dust, extending from about 2.5 au to 6 au, and constrained the properties of the inner dust component: e.g., a radially increasing surface density profile, and a depletion of 10^3 relative to the outer disk. Since self-shadowing and photoevaporation appears unlikely to be responsible for the au-sized gap of HD~139614, we thus tested if dynamical clearing could be a viable mechanism using hydrodynamical simulations to predict the gaseous disk structure. Indeed, a narrow au-sized gap is expected when a single giant planet interacts with the disk. Assuming that small dust grains are well coupled to the gas, we found that a ~ 3~Mjup planet located at 4.5 au from the star could, in less than 1 Myr, reproduce most of the aspects of the dust surface density profile, while no significant depletion in gas occurred in the inner disk, in contrast to the dust. However, the dust-depleted inner disk could be explained by the expected dust filtration by the gap and the efficient dust growth/fragmentation in the inner disk regions. Our results support the hypothesis of a giant planet opening a gap and shaping the inner region of the HD~139614 disk.
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