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Explore an advanced theoretical physics lecture presenting an effective solution to the 1D crossing equation for four identical scalars in conformal field theory. Learn about the universal constraints provided by 1D CFTs and discover how appropriate bases of functionals can transform the crossing equation into sum rules dual to extremal solutions that saturate positivity bounds. Examine the reconstruction of complete CFT data through a hybrid analytical-numerical method, and investigate how extremal solutions in specific limits naturally describe the flat space limit of quantum field theories in AdS2 space. Understand the bootstrapping process that connects CFT data with 2D S-matrices and vice-versa, while exploring the reconstruction of bulk AdS2 operators associated with extremal solutions. Gain insights into the largely unexplored space of 1D unitary CFTs and the powerful mathematical techniques used to analyze their structure and properties.
