Abstract

Over the past decade, perspectives from quantum information have shed valuable insight into the conjectured anti-de Sitter space/conformal field theory (AdS/CFT) correspondence in high-energy physics. In particular, a growing body of evidence suggests that (approximate) quantum error correction could be a mechanism underlying the holographic correspondence: local bulk AdS observables are encoded as operator algebraic quantum error correcting codes on a subspace of the boundary CFT Hilbert space and bulk AdS locality emerges from complementary recovery of the encoding boundary algebras. Motivated by this theory and a recent conjecture of Bousso et. al. on the bulk AdS description of boundary cocycle flow, we characterize (approximate) complementary recovery in terms of (approximate) intertwining of bulk and boundary cocycle derivatives. Using a recent framework of Dybalski-Wrochna, we then show that the aforementioned complementary recovery holds for Weyl algebras of Klein-Gordon fields in AdS wedges, yielding an operator algebraic version of subregion-subregion duality. Based on joint work with Monica Jinwoo Kang.