Integrable Wilson loops in ABJM: a Y-system computation of the cusp anomalous dimension

We study the integrability properties of Wilson loops in the N = 6 three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matrices that govern the interaction of spin-chain excitations with the boundary, including their dressing factors, and we check them against weak- and strong-coupling results. Furthermore, we propose a Y -system of equations for the cusped Wilson line of ABJM, and we use it to reproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-size correction. Finally, we write a set of BTBA equations consistent with the Y -system proposal.

Automated summary

We study the integrability properties of Wilson loops in the N = 6 three-dimensional Chern-Simons-matter (ABJM) theory. We construct an open spin chain and compute the reflection matrices to analyze the interaction and anomalous dimensions of operators. We also propose a Y-system and BTBA equations to verify the properties of Wilson loops in the ABJM theory.