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

TL;DR

This paper investigates Wilson loops in N=6 superconformal Chern-Simons theory, revealing their dual string descriptions, supersymmetry properties, and parallels with N=4 super Yang-Mills, providing insights into AdS/CFT correspondence.

Contribution

It classifies supersymmetric Wilson loops, analyzes their holographic duals, and proposes a matrix model for their expectation values, bridging weak and strong coupling regimes.

Findings

One combination of Wilson loops is dual to fundamental strings in AdS4 x CP3.

Circular Wilson loops exhibit vanishing odd loop diagrams, similar to N=4 SYM.

The expectation value is modeled by a Gaussian matrix model with an interpolating function.

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.