Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory

TL;DR

This paper investigates instanton effects on 1/6 BPS Wilson loops in ABJM theory using the Fermi gas approach, revealing connections to refined topological strings and instanton cancellation mechanisms.

Contribution

It introduces a detailed analysis of instanton corrections to Wilson loops in ABJM theory, linking membrane instantons to refined topological string theory and exploring pole cancellation.

Findings

Membrane instanton corrections are governed by refined topological strings in the Nekrasov-Shatashvili limit.

Pole cancellation between membrane and worldsheet instantons applies to Wilson loop VEVs.

Study extends to Wilson loops with two boundaries, broadening the understanding of instanton effects.

Abstract

We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.