Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals

TL;DR

This work analyzes 1/6-BPS Wilson loops in the 3D ${\cal N}=6$ Chern-Simons-matter theory (ABJM-like) and their string duals in type IIA on AdS_4 x CP^3. It builds a gauge-theory Wilson loop operator that couples to a specific scalar bilinear, establishes its supersymmetry properties, and computes its two-loop weak-coupling expectation value; at strong coupling, it identifies fundamental strings, D2-branes, and D6-branes as brane duals corresponding to different representations, with explicit actions and SUSY checks. The results show matching symmetry, charges, and preserved supersymmetries between the gauge theory operators and their AdS/CFT duals, including a smeared F1 configuration yielding 1/6-BPS status. The findings support the AdS/CFT correspondence for ABJM-like theories and provide a framework for understanding Wilson loops across representations via brane constructions, with potential for exact results and matrix-model descriptions in this 3D setting.

Abstract

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.

Figures (2)

• Figure 1: The two-loop Feynman diagrams contributing to a circular $\langle W\rangle$. The bold circular line represents the Wilson loop contour, whereas wiggly lines denote gluon and straight lines scalar propagators.
• Figure 2: Some examples of higher level N-gon tree graphs.