Chern-Simons theory from M5-branes and calibrated M2-branes

Understand

We study a sector of the 5d maximally supersymmetric Yang-Mills theory on $S^5$ consisting of $1/8$-BPS Wilson loop operators contained within a great $S^3$ inside $S^5$.

• We conjecture that these observables are described by a 3d Chern Simons theory on $S^3$, analytically continued to a pure imaginary Chern-Simons level.
• Therefore, the expectation values of these 5d Wilson loops compute knot invariants.
• We verify this conjecture in the weakly-coupled regime from explicit Feynman diagram computations.