Universal holographic Wilson loops in 3d SCFTs

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.