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We study light-like polygonal Wilson loops in three-dimensional Chern-Simonsand ABJM theory to two-loop order. For both theories we demonstrate that theone-loop contribution to these correlators cancels. For pure Chern-Simons, wefind that specific UV divergences arise from diagrams involving two cusps,implying the loss of finiteness and topological invariance at two-loop order.Studying those UV divergences we derive anomalous conformal Ward identities forn-cusped Wilson loops which restrict the finite part of the latter toconformally invariant functions. We also compute the four-cusp Wilson loop inABJM theory to two-loop order and find that the result is remarkably similar tothat of the corresponding Wilson loop in N=4 SYM. Finally, we speculate aboutthe existence of a Wilson loop/scattering amplitude relation in ABJM theory.

Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory