Uploaded December 2022 | Updated September 2026, 2 weeks ago
Classical phases of (0+1)-D unitary matrix models can be characterised by free Fermi droplets in two dimensions. Quantization of these droplets leads to a Hilbert space which nicely factorizes into two sectors–corresponding to the upper and lower Fermi surfaces. We will establish a concrete map between states of the Hilbert space and geometries of the droplet (with certain restrictions). We will demonstrate that correlation between two coherent states in each sector is equal to the chiral and anti-chiral partition function of 2D Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space admits a composite basis, we will show that correlation between two classical droplet geometries is equal to the full Yang-Mills partition function on a cylinder. We further establish a connection between higher point correlators in the Hilbert space and higher point correlators in 2D Yang-Mills on Riemann surface. We will also briefly discuss q-deformed Yang- Mills amplitude and how certain special droplet geometry correlators can be mapped to them without deforming the underlying gauge group. I will end with certain speculations about how instantonic corrections of Yang-Mills theories might be captured in the states of the Hilbert space obtained from the droplet geometry.
Presented by Debangshu Mukherjee 08-12-2022.
Classical phases of (0+1)-D unitary matrix models can be characterised by free Fermi droplets in two dimensions. Quantization of these droplets leads to a Hilbert space which nicely factorizes into two sectors–corresponding to the upper and lower Fermi surfaces. We will establish a concrete map between states of the Hilbert space and geometries of the droplet (with certain restrictions). We will demonstrate that correlation between two coherent states in each sector is equal to the chiral and anti-chiral partition function of 2D Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space admits a composite basis, we will show that correlation between two classical droplet geometries is equal to the full Yang-Mills partition function on a cylinder. We further establish a connection between higher point correlators in the Hilbert space and higher point correlators in 2D Yang-Mills on Riemann surface. We will also briefly discuss q-deformed Yang- Mills amplitude and how certain special droplet geometry correlators can be mapped to them without deforming the underlying gauge group. I will end with certain speculations about how instantonic corrections of Yang-Mills theories might be captured in the states of the Hilbert space obtained from the droplet geometry.
Presented by Debangshu Mukherjee 08-12-2022.
