May one wear tzitzis directly over one’s body without an undershirt or the like?
There is no formal prohibition on wearing tzitzis directly on one’s body.
However, many are particular to wear the tzitzis over an undershirt, so that the garment will not become sweaty and sullied (which is disrespectful for the tzitzis; see also sources), and not be in direct contact with the body.
See Kaf Hachaim 8:3, who writes, based on kabbalistic principles, that the tzitzis garment should not be worn on the flesh. This is also stated by Rav Chaim Kanievsky (Techeiles Ve’argaman 5), and by Teshuvos Vehanhagos (1:25), for fear that the garment would be considered an “undershirt,” which might be exempt from the obligation of tzitzis.