Holography and volume conjecture
imported>Pythagoras0님의 2014년 6월 10일 (화) 19:56 판
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
- M-theory : 11d physical theory
- fundamental objects are M2 (3d), M5(6d) branes
- in the study of dynamics of N M5-branes on $\mathbb{R}^{1,2}\times M$
- Terashima, Yuji, and Masahito Yamazaki. “SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls.” Journal of High Energy Physics 2011, no. 8 (August 2011). doi:10.1007/JHEP08(2011)135.
- 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.