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We report a study of the low-mass Class-0 multiple system VLA 1623AB in theOphiuchus star-forming region, using H$^{13}$CO$^+$ ($J=3-2$), CS ($J=5-4$),and CCH ($N=3-2$) lines as part of the ALMA Large Program FAUST. The analysisof the velocity fields revealed the rotation motion in the envelope and thevelocity gradients in the outflows (about 2000 au down to 50 au). We furtherinvestigated the rotation of the circum-binary VLA 1623A disk as well as theVLA 1623B disk. We found that the minor axis of the circum-binary disk of VLA1623A is misaligned by about 12 degrees with respect to the large-scale outflowand the rotation axis of the envelope. In contrast, the minor axis of thecircum-binary disk is parallel to the large-scale magnetic field according toprevious dust polarization observations, suggesting that the misalignment maybe caused by the different directions of the envelope rotation and the magneticfield. If the velocity gradient of the outflow is caused by rotation, theoutflow has a constant angular momentum and the launching radius is estimatedto be $5-16$ au, although it cannot be ruled out that the velocity gradient isdriven by entrainments of the two high-velocity outflows. Furthermore, wedetected for the first time a velocity gradient associated with rotation towardthe VLA 16293B disk. The velocity gradient is opposite to the one from thelarge-scale envelope, outflow, and circum-binary disk. The origin of itsopposite gradient is also discussed.

FAUST III. Misaligned rotations of the envelope, outflow, and disks in the multiple protostellar system of VLA 1623$-$2417