Holographical Description of BPS Wilson Loops in Flavored ABJM Theory

TL;DR

This paper explores holographic duals of BPS Wilson loops in flavored ABJM theory, identifying specific membrane configurations in M-theory that correspond to these loops and analyzing their supersymmetry properties.

Contribution

It provides a detailed holographic description of 1/3-BPS Wilson loops in flavored ABJM theory using M2-brane configurations in $AdS_4 imes N(1,1)$, including the computation of their expectation values.

Findings

Identified two 1/3-BPS membrane configurations.

One configuration matches the Gaiotto-Yin type Wilson loop.

No membranes with higher supersymmetry were found.

Abstract

As holographic description of BPS Wilson loops in ${\cal N}=3$ flavored ABJM theory with $N_f=k=1$, BPS M2-branes in $AdS_4\times N(1, 1)$ are studied in details. Two $1/3$-BPS membrane configurations are found. One of them is dual to the $1/3$-BPS Wilson loop of Gaiotto-Yin type. The regulated membrane action captures precisely the leading exponential behavior of the vacuum expectation values of $1/3$-BPS Wilson loops in the strong coupling limit, which was computed before using supersymmetric localization technique. Moreover, there is no BPS membrane with more supersymmetries in the background, under quite natural assumption on the membrane worldvolume. This suggests that there is no Wilson loop preserving more than 1/3 supersymmetries in such flavored ABJM theory.