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2D Conformal Field Theories and Holography | | Laurent Freidel
; Kirill Krasnov
; | | Date: |
10 May 2002 | | Journal: | J.Math.Phys. 45 (2004) 2378-2404 | | Subject: | hep-th | | Affiliation: | ENS-Lyon) and Kirill Krasnov (UCSB | | Abstract: | It is known that the chiral part of any 2d conformal field theory defines a 3d topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT relation exists also for the full CFT. The 3d topological theory that arises is a certain ``square’’ of the chiral TQFT. Such topological theories were studied by Turaev and Viro; they are related to 3d gravity. We establish an operator/state correspondence in which operators in the chiral TQFT correspond to states in the Turaev-Viro theory. We use this correspondence to interpret CFT correlation functions as particular quantum states of the Turaev-Viro theory. We compute the components of these states in the basis in the Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we obtain is a generalization of the Verlinde formula. The later is obtained from our expression for a zero colored graph. Our results give an interesting ``holographic’’ perspective on conformal field theories in 2 dimensions. | | Source: | arXiv, hep-th/0205091 | | Services: | Forum | Review | PDF | Favorites | |
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