Precision calculation of 1/4-BPS Wilson loops in AdS$_5\times S^5$

Understand

We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of "latitudes") in ${\cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5\times$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 Gel'fand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case.