Holography of wrapped M5-branes and Chern–Simons theory

We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d–3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern–Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N   limit. We check the correspondence numerically in a number of examples, and confirm the N3N3 scaling with precise coefficients.