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Explore holographic principles in quantum field theory through this 58-minute conference talk examining bulk-boundary local topological order (LTO) axioms for quantum spin systems. Learn how these axioms enable the definition of physical boundaries manifested by nets of boundary algebras in one dimension lower, establishing a formal framework for topological holography where braided tensor categories of DHR bimodules capture bulk topological order. Discover the extension of LTO axioms to quantum spin systems with topological boundaries, producing physical boundary algebras whose topological boundary DHR bimodules recover topological boundary order. Examine detailed analysis of Levin-Wen and Walker-Wang bulk-boundary systems, including the introduction of 2D braided categorical nets of algebras constructed from unitary braided fusion categories that arise as boundary algebras in Walker-Wang models. Investigate the canonical state corresponding to standard topological boundaries in Walker-Wang models, where cone von Neumann algebras exhibit type I characteristics with finite dimensional centers, contrasting with type II and III algebras from Levin-Wen models, while their superselection sectors recover the underlying unitary category structure and potentially capture fusion and braiding properties.
