Resumming planar diagrams for the N=6 ABJM cusped Wilson loop in light-cone gauge

Abstract

We analyse a light-like cusped Wilson loop in N=6 superconformal Chern-Simons theory at both weak and strong coupling in light-cone gauge. At the second order in the 't Hooft coupling $\lambda$ the correct cusp anomalous dimension $\Gamma_{\rm cusp}=-\phi / 2 \lambda^2$ is recovered through a deformation of the contour that takes both rays of the cusp slightly off of the light-cone. The strong coupling behaviour is addressed by means of the Bethe-Salpeter equation for ladders of tree-level gauge propagators and ladders of one-loop corrected gauge propagators. It turns out that, as might be expected, the contribution of Chern-Simons tree-level propagators is insensitive of the cusp angle $\phi$. On the other hand, corrected propagators lead to an exponential large $\lambda$ behaviour $\Gamma_{\rm cusp} \sim \exp\sqrt{\lambda\phi}$ which, though, disagrees with the AdS/CFT predictions in the power of $\phi$.