Holography and volume conjecture - 편집 역사

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imported>Pythagoras0: 새 문서: * 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/...

2014-06-11T02:14:18Z

새 문서: * 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/...

새 문서

* 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.

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* asymptotic behavior of perturbative Chern-Simons invariants on knot complements $M$
+* 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 $T[M]$
+* 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 <math>T[M]</math>
-* using holographic principle one can related the 3D theory $T[M]$ to M-theory on an anti de-Sitter space
+* using holographic principle one can related the 3D theory <math>T[M]</math> to M-theory on an anti de-Sitter space
@@ 9번째 줄: / 9번째 줄: @@
 * 11d physical theory
 * fundamental objects are M2 (3d), M5(6d) branes
-* let $M$ be a 3dimensional space obtained as knot complement
+* let <math>M</math> be a 3dimensional space obtained as knot complement
-* in the study of dynamics of N M5-branes on $\mathbb{R}^{1,2}\times M$
+* in the study of dynamics of N M5-branes on <math>\mathbb{R}^{1,2}\times M</math>
 ==3d-3d correspondence==
-* partition function $T_N[M]$ on $S_b^3$ = partition function $PGL(N)$ CS theory on $M$
+* 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 $2\pi i b^2=\hbar$
+where <math>2\pi i b^2=\hbar</math>
 ==holographic principle==
-* 3d $T_N[M]$ theory at large $N$ = M-theory on $\operatorname{AdS}_4\times M\times S^4$
+* 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 $N$
+* 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>

← 이전 판		2020년 11월 13일 (금) 14:18 판
41번째 줄:		41번째 줄:
	===holography===		===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.		* 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]]

@@ 3번째 줄: / 3번째 줄: @@
 * 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 $T_N[M]$ theory at large $N$ = M-theory on $\operatorname{AdS}_4\times M\times S^4$
-==3d-3d correspondence==
+==articles==
-* M-theory : 11d physical theory
+* 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.
-* fundamental objects are M2 (3d), M5(6d) branes
+===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.

← 이전 판		2014년 6월 11일 (수) 02:56 판
11번째 줄:		11번째 줄:

	==3d-3d correspondence==		==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.		* 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.

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* asymptotic behavior of perturbative Chern-Simons invariants kn know complements $M$
+* 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