Holography of 3d-3d correspondence at Large N

Understand

We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold.

• On the one hand, it leads to the 3d-3d correspondence which maps an $\mathcal{N}=2$ superconformal field theory to a pure Chern-Simons theory on the 3-manifold.
• On the other hand, it leads to a warped AdS$_4$ geometry in M-theory holographically dual to the superconformal field theory.
• Combining the holographic duality and the 3d-3d correspondence, we propose a conjecture for the large $N$ limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold.