Using zeta-function regularization, we study the one-loop effective action of fundamental strings in AdS5 xS5 dual to the latitude 1/4-BPS Wilson loop in N=4 super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic 1/2-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.Instituto de Física La Plata