From 2D Droplets to 2D Yang-Mills: Quantum Mechanics and Geometry Connections - Lecture

Explore a comprehensive lecture on the connection between 2D droplets and 2D Yang-Mills theory. Delve into the characterization of classical phases in (0+1)-D unitary matrix models using free Fermi droplets in two dimensions. Examine the quantization of these droplets and the resulting Hilbert space factorization into upper and lower Fermi surface sectors. Discover the concrete mapping between Hilbert space states and droplet geometries, with specific restrictions. Investigate the correlation between coherent states in each sector and its relationship to chiral and anti-chiral partition functions of 2D Yang-Mills theory on a cylinder. Learn how the full Hilbert space's composite basis leads to correlations between classical droplet geometries equaling the complete Yang-Mills partition function on a cylinder. Explore the connection between higher-point correlators in the Hilbert space and 2D Yang-Mills on Riemann surfaces. Briefly examine q-deformed Yang-Mills amplitudes and their relation to special droplet geometry correlators. Conclude with speculations on capturing instantonic corrections of Yang-Mills theories through droplet geometry-derived Hilbert space states. Topics covered include unitary matrix quantum mechanics, 2D angles, phase space, classical solutions, coherent states, Young diagram basis, and cylinder amplitudes.