Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual (0809.3786v2)

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.

Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in AdS Supergravity Dual

The paper by Soo-Jong Rey, Takao Suyama, and Satoshi Yamaguchi provides a comprehensive analysis of Wilson loop operators in the context of three-dimensional, $\mathcal{N}=6$ superconformal Chern-Simons theory, which is dual to type IIA superstring theory on $\text{AdS}_4 \times \mathbb{CP}^3$. This research contributes to the ongoing investigation into the AdS/CFT correspondence, offering insights into the behavior of Wilson loops and their holographic interpretations.

Key Findings and Contributions

1. Wilson Loop Operators: The paper introduces novel Wilson loop operators in the ABJM theory, distinguishing themselves by their transformation properties under time-reversal symmetry. For any given contour, the paper identifies two linear combinations of Wilson loops that transform oppositely under time-reversal. This duality is crucial for understanding their correspondence with fundamental strings in type IIA superstring theory. One combination is shown to be holographically dual to a fundamental string, while the orthogonal combination is set to zero.
2. Supersymmetry and Classification: The authors classify the supersymmetric Wilson loops and find that their maximum supersymmetry is $\frac{1}{6}$ of the $\mathcal{N}=6$ superconformal symmetry. This classification enhances our understanding of symmetry preservation in both the gauge theory and its string dual.
3. Perturbative Analysis: An exploration of the Wilson loop expectation value under planar perturbation theory is provided, revealing intriguing parallels with $\mathcal{N}=4$ super Yang-Mills theory. Notably, all odd loop diagrams vanish, while even loops yield nontrivial contributions, suggesting a similar weak-strong coupling behavior.
4. Holographic Duality and Interpolating Functions: By examining the expected values of circular Wilson loops, the authors propose an interesting connection to zero-dimensional Gaussian matrix models, with an interpolating function of 't Hooft coupling $\lambda$. This function bridges the weak and strong coupling regimes, thereby offering a novel testing ground for the AdS/CFT correspondence.

Implications and Future Directions

The research opens new avenues for testing the AdS/CFT correspondence within the framework of ABJM theory. The parallels with $\mathcal{N}=4$ super Yang-Mills suggest broader applicability of techniques used in four-dimensional theories to three-dimensional contexts.

Future research can target several open questions, such as:

• The exploration of other supersymmetric Wilson loops with enhanced symmetry preservation (e.g. $\mathcal{N}=2$ superconformal Chern-Simons theories).
• The potential applications of the interpolating function $f(\lambda)$ in other realms of gauge physics, possibly relating it to observables like static quark potentials or amplitudes.
• Calculating higher-order perturbative contributions to test the propositions about matrix model equivalences more rigorously.

Conclusion

This paper enhances the understanding of superconformal Chern-Simons theories and their string duals, providing a clear analytical framework for examining Wilson loops through both perturbative approaches and holographic duality. This work should stimulate numerous discussions and inspire further research into gauge/gravity correspondence, symmetries in Chern-Simons theories, and the precise behaviors of Wilson loops in various dimensions.