A kinematically detected planet candidate in a transition disk

Context. Transition disks are protoplanetary disks with inner cavities possibly cleared by massive companions. Observing them at high resolution is ideal for mapping their velocity structure and probing companion-disk interactions.Aims. We present Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 dust and gas observations of the transition disk around RXJ1604.3-2130 A, known to feature nearly symmetric shadows in scattered light, and aim to search for non-Keplerian features.Methods. We studied the (CO)-C-12 line channel maps and moment maps of the line-of-sight velocity and peak intensity. We fitted a Keplerian model of the channel-by-channel emission to study line profile differences and produced deprojected radial profiles for all velocity components.Results. The (CO)-C-12 emission is detected out to R similar to 1.8 '' (265 au). It shows a cavity inward of 0.39 '' (56 au) and within the dust continuum ring (at similar to 0.56 '', i.e., 81 au). Azimuthal brightness variations in the (CO)-C-12 line and dust continuum are broadly aligned with the shadows detected in scattered-light observations. We find a strong localized non-Keplerian feature toward the west within the continuum ring (at R = 41 +/- 10 au and PA = 280 +/- 2 degrees). It accounts for delta v(phi)/v(kep) similar to 0.4 or delta v(z)/v(kep) similar to 0.04, depending on if the perturbation is in the rotational or vertical direction. A tightly wound spiral is also detected and extends over 300 degrees in azimuth, possibly connected to the localized non-Keplerian feature. Finally, a bending of the iso-velocity contours within the gas cavity indicates a highly perturbed inner region, possibly related to the presence of a misaligned inner disk.Conclusions. While broadly aligned with the scattered-light shadows, the localized non-Keplerian feature cannot be solely due to changes in temperature. Instead, we interpret the kinematical feature as tracing a massive companion located at the edge of the dust continuum ring. We speculate that the spiral is caused by buoyancy resonances driven by planet-disk interactions. However, this potential planet at similar to 41 au cannot explain the gas-depleted cavity, the low accretion rate, and the misaligned inner disk, which suggests the presence of another companion closer in.