Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory

Understand

In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order.

• Here we study light-like polygonal Wilson loops with n cusps in planar three-dimensional Chern-Simons and ABJM theory to two loops.
• Remarkably, the result in ABJM theory precisely agrees with the corresponding Wilson loop in N = 4 SYM at one-loop order for arbitrary n.
• In particular, anomalous conformal Ward identites allow for a so-called remainder function of conformal cross ratios, which is found to be trivial at two loops in ABJM theory in the same way as it is trivial in N = 4 SYM at one-loop order.