Hydrodynamics of the Chiral Dirac Spectrum

Understand

We derive a hydrodynamical description of the eigenvalues of the chiral Dirac spectrum in the vacuum and in the large $N$ (volume) limit.

• The linearized hydrodynamics supports sound waves.
• The stochastic relaxation of the eigenvalues is captured by a hydrodynamical instanton configuration which follows from a pertinent form of Euler equation.
• The relaxation from a phase of localized eigenvalues and unbroken chiral symmetry to a phase of de-localized eigenvalues and broken chiral symmetry occurs over a time set by the speed of sound.