A note on multiply wound BPS Wilson loops in ABJM

TL;DR

This paper computes the expectation values of multiply wound BPS Wilson loops in planar ABJM theory at various loop orders, analyzing framing dependence and confirming results with localization and matrix model predictions.

Contribution

It provides explicit perturbative calculations of multiply wound BPS Wilson loops in ABJM theory, including framing dependence and comparison with localization results.

Findings

Agreement with localization at framing 1 for 1/6-BPS loops

Extraction of framing dependence for 1/2-BPS loops

Explicit multi-loop expectation values for multiply wound loops

Abstract

We consider BPS Wilson loops in planar ABJM theory, wound multiple times around the great circle. We compute the expectation value of the 1/6-BPS and 1/2-BPS Wilson loops to three- and two-loop order in perturbation theory, respectively, dealing with the combinatorics of multiple winding via recursive relations. For the 1/6-BPS Wilson loop we perform the computation at generic framing and at framing 1 we find agreement with the localization result. For the 1/2-BPS Wilson loop we compute the expectation value at trivial framing and by comparison with the matrix model expression we extract the framing dependence of the fermion diagrams.