Question:
Can you wear a tzitzit on the shirtless body underneath?
Answer:
The reason why it is customary to wear an undershirt underneath the tzitzis is because ןf the tzitizis are up against the body they will become like a garment for absorbing sweat, which according to some poskim is degrading to the tzitzis. This is the preferred thing to do, however if it is hot, it is permitted to wear the tzitzis on the skin in a temporary manner see Rivivos Efrayim 4-15.
Sources:
Also see Piskei Teshuvos 8-22 in the name of Arizal. Halichos Shlomo (Tefillah 3-11) though says that it is not an embarrassment to the mitzva and it is permitted. Even according to this opinion, the actual tzitzis strings should be on the outside so they can be seen.
