Wilson loops, M2-branes and strings

Abstract

We establish a universal approach for studying the semiclassical quantization of both probe M2-branes and fundamental strings in asymptotically AdS$_{4}$ backgrounds. On the field theory side, their partition functions are dual to the vacuum expectation value of half-BPS Wilson loops of a class of three-dimensional $\mathcal{N}\geq 2$ Chern-Simons-matter theories. Utilizing this universal approach we arrive at novel predictions for the semiclassical behaviour of the Wilson loop or upon availability match our results with the previously obtained expressions via supersymmetric localization. We also show that the correct choice of holographic ensemble suggests that the semiclassical quantization of probe M2-branes yields the full perturbative answer in the rank of the gauge group $N$ for the dual Wilson loop. This is a proceedings contribution to the ''Athens Workshop in Theoretical Physics: 10th Anniversary'', held at the National and Kapodistrian University of Athens on December 17-19 2025.