"Holography and volume conjecture"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| (다른 사용자 한 명의 중간 판 2개는 보이지 않습니다) | |||
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==introduction== | ==introduction== | ||
| − | * asymptotic behavior of perturbative Chern-Simons invariants on knot complements | + | * asymptotic behavior of perturbative Chern-Simons invariants on knot complements <math>M</math> |
| − | * 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 | + | * 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 <math>T[M]</math> |
| − | * using holographic principle one can related the 3D theory | + | * using holographic principle one can related the 3D theory <math>T[M]</math> to M-theory on an anti de-Sitter space |
| + | |||
| + | |||
| + | ==M-theory== | ||
| + | * still mysterious | ||
| + | * 11d physical theory | ||
| + | * fundamental objects are M2 (3d), M5(6d) branes | ||
| + | * let <math>M</math> be a 3dimensional space obtained as knot complement | ||
| + | * in the study of dynamics of N M5-branes on <math>\mathbb{R}^{1,2}\times M</math> | ||
| + | |||
| + | |||
| + | ==3d-3d correspondence== | ||
| + | * partition function <math>T_N[M]</math> on <math>S_b^3</math> = partition function <math>PGL(N)</math> CS theory on <math>M</math> | ||
| + | :<math> | ||
| + | Z_{T_N[M]}[S_b^3](N,M;b)=Z^{\text{geom}}_{PGL(N)}[M;\hbar] | ||
| + | </math> | ||
| + | where <math>2\pi i b^2=\hbar</math> | ||
==holographic principle== | ==holographic principle== | ||
| − | * | + | * 3d <math>T_N[M]</math> theory at large <math>N</math> = M-theory on <math>\operatorname{AdS}_4\times M\times S^4</math> |
| + | * for large <math>N</math> | ||
| + | :<math> | ||
| + | Z_{T_N[M]}[S_b^3](N,M;b)=\exp(-S_0^{\text{gravity}}[\operatorname{AdS}_4\times M\times S^4])\frac{(b+b^{-1})^2N^3}{12\pi}\operatorname{Vol}(M)+\text{subleadings} | ||
| + | </math> | ||
| + | |||
| + | |||
| + | ==related items== | ||
| + | * [[AdS/CFT correspondence]] | ||
| − | == | + | ==articles== |
| − | * | + | * Gang, Dongmin, Nakwoo Kim, and Sangmin Lee. “Holography of Wrapped M5-Branes and Chern-Simons Theory.” arXiv:1401.3595 [hep-Th], January 15, 2014. http://arxiv.org/abs/1401.3595. |
| − | + | ===3d-3d correspondence=== | |
| − | |||
* 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. | * 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. | * 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. | ||
| + | ===holography=== | ||
| + | * 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. | ||
| + | [[분류:migrate]] | ||
2020년 11월 16일 (월) 05:29 기준 최신판
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
M-theory
- still mysterious
- 11d physical theory
- fundamental objects are M2 (3d), M5(6d) branes
- let \(M\) be a 3dimensional space obtained as knot complement
- in the study of dynamics of N M5-branes on \(\mathbb{R}^{1,2}\times M\)
3d-3d correspondence
- partition function \(T_N[M]\) on \(S_b^3\) = partition function \(PGL(N)\) CS theory on \(M\)
\[ Z_{T_N[M]}[S_b^3](N,M;b)=Z^{\text{geom}}_{PGL(N)}[M;\hbar] \] where \(2\pi i b^2=\hbar\)
holographic principle
- 3d \(T_N[M]\) theory at large \(N\) = M-theory on \(\operatorname{AdS}_4\times M\times S^4\)
- for large \(N\)
\[ Z_{T_N[M]}[S_b^3](N,M;b)=\exp(-S_0^{\text{gravity}}[\operatorname{AdS}_4\times M\times S^4])\frac{(b+b^{-1})^2N^3}{12\pi}\operatorname{Vol}(M)+\text{subleadings} \]
articles
- Gang, Dongmin, Nakwoo Kim, and Sangmin Lee. “Holography of Wrapped M5-Branes and Chern-Simons Theory.” arXiv:1401.3595 [hep-Th], January 15, 2014. http://arxiv.org/abs/1401.3595.
3d-3d correspondence
- 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.
holography
- 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.