Holography and volume conjecture

introduction

• asymptotic behavior of perturbative Chern-Simons invariants on knot complements $M$
• 3D-3D correspondence relates the CS invariants on M to supersymmetric quantities of the corresponding 3-dimensional quantum field theory which will be denoted by $T[M]$
• using holographic principle one can related the 3D theory $T[M]$ to M-theory on an anti de-Sitter space

holographic principle

• Maldacena, Juan M. “The Large N Limit of Superconformal Field Theories and Supergravity.” arXiv:hep-th/9711200, November 27, 1997. http://arxiv.org/abs/hep-th/9711200.

3d-3d correspondence

• Dimofte, Tudor, Davide Gaiotto, and Sergei Gukov. “Gauge Theories Labelled by Three-Manifolds.” arXiv:1108.4389 [hep-Th], August 22, 2011. http://arxiv.org/abs/1108.4389.