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

Journal of High Energy Physics, Feb 2016

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.

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V. Forini, V. Giangreco M. Puletti, L. Griguolo, D. Seminara, E. Vescovi. Precision calculation of 1/4-BPS Wilson loops in AdS5×S5, Journal of High Energy Physics, 2016, 105, DOI: 10.1007/JHEP02(2016)105