An exact limit of ABJM

TL;DR

This paper exactly solves certain Wilson loop expectation values in a special limit of planar ABJM theory, providing new insights into its integrability and related physical quantities.

Contribution

It introduces a method for exact calculation of Wilson loops and related quantities in a specific ABJM limit, confirming a conjecture on the dilatation operator.

Findings

Exact computation of Wilson loops on arbitrary contours

Determination of the cusp anomalous dimension and Bremsstrahlung function

Proof of a conjecture on the dilatation operator and integrability

Abstract

We study planar ABJM in a limit where one coupling is negligible compared to the other. We provide a recipe for exactly solving the expectation value of bosonic BPS Wilson loops on arbitrary smooth contours, or the leading divergence for cusped ones, using results from localization. As an application, we compute the exact (generalized) cusp anomalous dimension and Bremsstrahlung function and use it to determine the interpolating $h$-function. We finally prove a conjecture on the exact form of the dilatation operator in a closed sector, hinting at the integrability of this limit.