Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

TL;DR

It is proposed that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them and the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation.

Abstract

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.