2012/09/14 by Brian Swingle, Swingle, Brian · 53 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Duality (order theory) #Holography #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum entanglement #Quantum mechanics #Renormalization #Spacetime #Theoretical physics #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1209.3304
published in arXiv (Cornell University) 2013 (Cornell University)
arxiv created 2012/09/14 · openalex publication_date 2012/09/14 · arxiv updated 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large N limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large N limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large N theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).