Special flow equation and the GKP–Witten relation Supersymmetric gauge theories and the AdS/CFT correspondence
Sinya Aoki (Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, , Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502, , Japan); Janos Balog (Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, , PO Box 49, H-1525 Budapest 114, , Hungary); Tetsuya Onogi (Department of Physics, Osaka University, , Toyonaka, Osaka 560-0043, , Japan); Shuichi Yokoyama (Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, , Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502, , Japan)
Abstract We develop a framework for the reconstruction of the bulk theory dual to conformal field theory without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free-flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation for O(N) vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP–Witten relation concurrently emerge in this framework.
