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

TL;DR

This paper investigates light-like polygonal Wilson loops in 3D Chern-Simons and ABJM theories at two-loop order, revealing cancellations, divergences, and conformal properties, and draws parallels with N=4 SYM results.

Contribution

It provides the first two-loop analysis of light-like Wilson loops in these theories, uncovering divergence structures and conformal constraints, and compares ABJM results to N=4 SYM.

Findings

One-loop contributions cancel in both theories.

UV divergences appear at two loops, affecting finiteness.

ABJM Wilson loops resemble N=4 SYM results.

Abstract

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. We also compute the four-cusp Wilson loop in ABJM theory to two-loop order and find that the result is remarkably similar to that of the corresponding Wilson loop in N=4 SYM. Finally, we speculate about the existence of a Wilson loop/scattering amplitude relation in ABJM theory.