Holography of 3d-3d correspondence at Large N

Abstract

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. The conjecture claims that the tree, one-loop and two-loop terms all share the same $N^3$ scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large $N$. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the suppression of higher loop terms in a few examples.

37 pages, 7 figures

References in corpus (7)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The gravity duals of N=2 superconformal field theories
• Wrapped M5-branes, consistent truncations and AdS/CMT
• Instantons on the 5-sphere and M5-branes
• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• BPS M5-branes as Defects for the 3d-3d Correspondence
• Wilson loops on three-manifolds and their M2-brane duals

Cited by in corpus (3)

• Non-Perturbative Defects in Tensor Models from Melonic Trees
• RG flows from (1,0) 6D SCFTs to N=1 SCFTs in four and three dimensions
• Wrapped $M5$-branes and complex saddle points