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Explore advanced concepts in three-dimensional Anti-de Sitter space and two-dimensional conformal field theory correspondence through this comprehensive lecture delivered by Alejandra Castro from Cambridge University's Department of Applied Mathematics and Theoretical Physics. Delve into the fundamental role of symmetries in holographic duality, examining how symmetry principles govern the relationship between gravitational theories in AdS₃ space and conformal field theories on its two-dimensional boundary. Learn about the mathematical frameworks that underpin this correspondence, including the structure of conformal symmetries, the role of diffeomorphisms, and how these symmetries manifest in both the bulk gravitational theory and boundary field theory. Investigate specific applications of symmetry analysis in understanding black hole physics, thermodynamics, and quantum information aspects within the AdS₃/CFT₂ context. Discover how symmetry considerations provide powerful tools for computing correlation functions, understanding entanglement properties, and analyzing the emergence of spacetime from quantum field theory. This second class in the series builds upon foundational concepts to present more sophisticated techniques and recent developments in the field, making it essential viewing for graduate students and researchers working in string theory, quantum gravity, and holographic duality.
