Renormalization Group Flow in Algebraic Holography

The remarkable scaling properties of the AdSCFT correspondence[5] have been proven extremely useful as a calculational device for the scaling behaviour of holographic pairs, known as the Holographic Renormalization Group (RG). In this communication, the aforementioned scaling properties will be studied in a somewhat different context. We’ll adopt the formalism of Local Quantum Physics[1], in terms of C*-algebras of local observables, for which a structural (i.e., model-independent) form of the AdS-CFT correspondence has been proven by Rehren. This form, called Algebraic Holography or Rehren duality, is, however, a statement for local observables in a fixed spacetime background: some aspects that are linked to unrestricted general covariance, such as conformal anomalies[4], are quite obscure in our setting. Nevertheless, it will be shown that other phenomena, such as the UV/IR connection[8] and the very duality between the dynamics between different leaves of the Poincaré foliation of anti-de Sitter (AdS) spacetime and the RG flow of the boundary (Minkowski) theory, here appear naturally.