Flow equation, conformal symmetry and AdS geometry

Abstract

We argue that the Anti-de-Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.

10 pages, no figures, v2: minor improvements, published version

References in corpus (4)

• Gravitation from Entanglement in Holographic CFTs
• Infinite N phase transitions in continuum Wilson loop operators
• Holographic description of large N gauge theory
• Geometries from field theories

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• Perturbative analysis of the Wess-Zumino flow
• AdS/CFT correspondence for the $O(N)$ invariant critical ${\phi }^4$ model in 3-dimensions by the conformal smearing