Holography of 3d-3d correspondence at large N

Open Access
Regular Article - Theoretical Physics

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 AdS4 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 N3 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.

Keywords

Gauge-gravity correspondence Chern-Simons Theories M-Theory 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.School of PhysicsKorea Institute for Advanced StudySeoulSouth Korea
  2. 2.Department of Physics and Research Institute of Basic ScienceKyung Hee UniversitySeoulSouth Korea
  3. 3.Center for Theoretical Physics, Department of Physics and Astronomy, College of Liberal StudiesSeoul National UniversitySeoulSouth Korea

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