Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual

TL;DR

<1> This work identifies Wilson loop operators in the ABJM theory that come in two linear combinations transforming oppositely under generalized time-reversal, and argues that the properly chosen combination is dual to a fundamental string in AdS4 x CP3, while the orthogonal combination vanishes. <2> It shows that the only preserved SUSY Wilson loop is ${1\over6}$-BPS, and demonstrates a perturbative structure for the circular loop where odd orders vanish and even orders decompose into a ${\cal N}=4$ SYM-like ladder part and a pure Chern-Simons knot part, suggesting a factorization into a pure CS result times a Gaussian matrix model with a variance given by an interpolating function $f(\lambda)$. <3> The paper develops a Gaussian matrix-model reduction for the ladder sector, discusses the exact CS contribution, and proposes how a smooth interpolation $f(\lambda)$ ties weak and strong coupling results, providing a new testbed for AdS/CFT in the ABJM context. <4> It also analyzes time-reversal and D2-brane interpretations, outlines a path toward possible localization, and identifies several open questions related to symmetry, smearing in CP3, and higher-loop structure.</paper_summary>

Abstract

We study Wilson loop operators in three-dimensional, N=6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS4 x CP3. Novelty of Wilson loop operators in this theory is that, for a given contour, there are two linear combinations of Wilson loop transforming oppositely under time-reversal transformation. We show that one combination is holographically dual to IIA fundamental string, while orthogonal combination is set to zero. We gather supporting evidences from detailed comparative study of generalized time-reversal transformations in both D2-brane worldvolume and ABJM theories. We then classify supersymmetric Wilson loops and find at most 1/6-supersymmetry. We next study Wilson loop expectation value in planar perturbation theory. For circular Wilson loop, we find features remarkably parallel to circular Wilson loop in N=4 super Yang-Mills theory in four dimensions. First, all odd loop diagrams vanish identically and even loops contribute nontrivial contributions. Second, quantum corrected gauge and scalar propagators take the same form as those of N=4 super Yang-Mills theory. Combining these results, we propose that expectation value of circular Wilson loop is given by Wilson loop expectation value in pure Chern-Simons theory times zero-dimensional Gaussian matrix model whose variance is specified by an interpolating function of `t Hooft coupling. We suggest the function interpolates smoothly between weak and strong coupling regime, offering new test ground of the AdS/CFT correspondence.

Figures (8)

• Figure 1: The Feynman diagrams contributing at order $\lambda^1$.
• Figure 2: The Feynman diagrams contributing at order $\lambda^2$.
• Figure 3: One loop photon self energy diagrams from bosons, Faddeev-Popov ghosts, gauge bosons, fermions, respectively. Contributions of boson tadpole vanishes identically. Contributions of Faddeev-Popov ghosts and gauge bosons cancel each other.
• Figure 4: The diagrams of order $\lambda^3$ which vanish by themselves.
• Figure 5: The Feynman diagrams contributing to order $\lambda^3$. They all have two vertices of the Wilson loop along the contour $C$.