Precision calculation of 1/4-BPS Wilson loops in AdS5 x S5

We study the strong coupling behaviour of 1/4-BPS circular Wilson loops (a family of latitudes) in A1 = 4 Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS(5) x S-5. Supersymmetric localization provides an exact result that, in the large 't Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the ratio between the generic latitude and the maximal 1/2-BPS circle: any measure-related ambiguity should simply cancel in this way. We use the Gel'fand-Yaglom method with Dirichlet boundary conditions to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: the difference is encoded into a precise remainder function. We comment on the possible origin and resolution of this discordance.