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

Abstract

We study the integrability properties of Wilson loops in the N = 6 threedimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of anopen spin chain that describes the anomalous dimensions of operators inserted along thecontour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matricesthat govern the interaction of spin-chain excitations with the boundary, including theirdressing 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 toreproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-sizecorrection. Finally, we write a set of BTBA equations consistent with the Y -system proposal.