Explore holographic conformal field theories and strongly coupled AdS matter in this 46-minute conference talk by Alex Belin from the University of Milan. Delve into the latest developments in conformal field theory language, including insights from the conformal bootstrap program, as part of the "Gravity from algebra: modern field theory methods for holography" conference at KITP. Examine the relationship between consistency conditions in quantum gravity and CFT, and their potential connection to string/M-theory. Cover topics such as large N bootstrap, holographic CFTs dual to general relativity, CFT sum rules, gravitational effective field theory, supersymmetry in holography, low-dimensional holography, modularity, quantum chaos, black holes from strongly-coupled finite temperature physics, symmetry constraints on gravitational path integrals, AdS vacua, S-matrices, and their relation to CFT correlators. Gain insights into the two-step process, holographic conditions, large gap and delta gap conditions, factorization, multitraces, boundary terms, and the role of conformal symmetry in strongly coupled theories. Read more