Title: From 2D droplets to 2D Yang-Mills

Abstract: 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.

Talk – Video

Talk – Slides