Universal holographic Wilson loops in 3d SCFTs

TL;DR

This paper analyzes the expectation values of half-BPS Wilson loops in 3d superconformal theories with holographic duals, providing a universal semiclassical framework and conjecturing a full perturbative form for M-theory duals.

Contribution

It introduces a universal semiclassical description for Wilson loops in 3d SCFTs with M-theory and type IIA duals, and conjectures a complete perturbative expression for M-theory cases.

Findings

Derived the one-loop partition functions for M2-branes and strings.

Predicted large N behavior of Wilson loops in dual SCFTs.

Conjectured a full perturbative completion as a ratio of Airy functions for M-theory duals.

Abstract

We study the vacuum expectation value of half-BPS Wilson loop operators in two families of superconformal $\mathcal{N}=2$ Chern-Simons-matter theories. The first family is dual to AdS$_{4}$ solutions in M-theory, while the second one has a dual description in massive type IIA string theory. Utilizing the properties of the underlying geometry, we provide a universal description for the semiclassical quantization of a probe M2-brane and fundamental string in the respective holographic dual geometries. As a result, we find the one-loop partition function of both the M2-brane and the string which leads to a prediction for the large $N$ behaviour of the Wilson loops in the dual SCFTs. For theories with M-theory duals, we conjecture the full perturbative completion as a ratio of Airy functions.