Squeezed in three dimensions, moving in two: Hydrodynamic theory of 3D incompressible easy-plane polar active fluids

We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible polar active fluids. We show that the hydrodynamic model for this system belongs to the same universality class as that of an equilibrium system, namely a special 3D anisotropic magnet. The latter can be further mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding columnar phase. Through these connections we find a divergent renormalization of the damping coefficients in 3D easy-plane incompressible polar active fluids, and obtain their equal-time velocity correlation functions.