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

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