A two-loop octagon Wilson loop in $ \mathcal{N} = 4 $ SYM

Abstract

In the planar \( \mathcal{N} = 4 \) supersymmetric Yang-Mills theory at weak coupling, we perform the first analytic computation of a two-loop eight-edged Wilson loop embedded into the boundary of AdS 3. Its remainder function is given as a function of uniform transcendental weight four in terms of a constant plus a product of four logarithms. We compare to the strong-coupling result, and test a conjecture on the universality of the remainder function proposed in the literature.