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Delve into the intricate world of holographic conformal field theories (CFTs) in this extensive lecture, part 3 of a 5-part series. Explore advanced concepts and recent developments in the field, examining the space of holographic CFTs and their implications for our understanding of quantum gravity and string theory. Gain insights into the mathematical structures and physical principles that underpin these theories, and discover how they contribute to our broader comprehension of fundamental physics.