Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory

TL;DR

This work investigates supersymmetric Wilson loops in the ${ m ABJM}$ theory, a three-dimensional ${ m N}=6$ Chern-Simons-matter theory with gauge group $U_1(N) imes U_2(N)$. It constructs $1/6$-BPS Wilson loop operators that couple gauge fields to matter bilinears and analyzes their SUSY constraints, performing a perturbative expansion in the 't Hooft coupling $oldsymbol{\lambda}=N/k$ up to $oldsymbol{\lambda^2}$ in the planar limit. On the holographic side, a fundamental string solution in type IIA on ${ m AdS}_4 imes { m CP}^3$ ending on a circle yields an on-shell action $S_{ ext{NG}}=-oldsymbol{\pi}\sqrt{2oldsymbol{\lambda}}$, consistent with a dual half-BPS Wilson loop. The paper also outlines future directions, including the search for other BPS Wilson loops and higher-dimensional brane duals that encode representations beyond the fundamental. The analysis deepens the connection between Wilson loops in ABJM and their AdS/CFT duals, highlighting how perturbative and string-theoretic techniques illuminate nontrivial observables in three dimensions.

Abstract

We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS_4/CFT_3 correspondence. We first construct some supersymmetric Wilson loops. The perturbative computations are performed in the field theory side at the first two orders. A fundamental string solution ending on a circular loop is also studied.

Figures (4)

• Figure 1: The only contributing diagram at the order of $\lambda$.
• Figure 2: The contributing diagrams at the order of $\lambda^2$.
• Figure 3: One-matter-loop correction to the gluon propagator.
• Figure 4: Some needed Feynman rules