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

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Cited by in corpus (24)

• Holographic duals of 3d S-fold CFTs
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Rotating Black Hole Entropy from M5-branes
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Aspects of Defects in 3d-3d Correspondence
• A slow review of the AGT correspondence
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Teichmuller TQFT vs Chern-Simons Theory
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Aspects of AdS${}_2$ classification in M-theory: Solutions with mesonic and baryonic charges
• S-duality resurgence in SL(2) Chern-Simons theory
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• Taming Supersymmetric Defects in 3d-3d Correspondence
• RG flows from (1,0) 6D SCFTs to N=1 SCFTs in four and three dimensions
• Solving Mass-deformed Holography Perturbatively
• A perturbative study of holographic mABJM theory
• 3D-3D Correspondence from Seifert Fibering Operators
• Wrapped $M5$-branes and complex saddle points