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

Understand

We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order.

• For both theories we demonstrate that the one-loop contribution to these correlators cancels.
• For pure Chern-Simons, we find 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 for n-cusped Wilson loops which restrict the finite part of the latter to conformally invariant functions.