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Explore the rigorous mathematical foundations of Schwarzian Field Theory in this comprehensive lecture that bridges quantum field theory with probability theory. Delve into the theoretical framework of a quantum field theory that has garnered significant attention in physics literature, particularly in contexts involving two-dimensional quantum gravity, black holes, and AdS/CFT correspondence. Examine the universal nature of this theory and its emergence in systems with conformal symmetry, including detailed discussions of the Sachdev-Ye-Kitaev random matrix model and Jackie-Teitelboim gravity. Learn about recent mathematical advances in constructing rigorous foundations for Schwarzian Field Theory, including the formal construction of corresponding measures and systematic calculation methods for partition functions. Discover techniques for computing correlation functions within this theoretical framework and understand the application of large deviation principles to this quantum field theory. Gain insights into how probabilistic methods can be applied to establish mathematical rigor in quantum field theories that arise in modern theoretical physics, particularly those connected to gravity and conformal field theory.
