Precision calculation of 1/4-BPS Wilson loops in AdS 5 ×S 5

We study the strong coupling behaviour of 1/4-bps circular wilson loops (a family of “latitudes”) in $$ mathcal{n}=4 $$ super yang-mills theory, computing the one-loop corrections to the relevant classical string solutions in ads5 ×s5. 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.