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We consider relativistic non-Abelian superfluids, where the expectation valueof the global symmetry currents relate space and internal indices, thuscreating a "locked" phase. Locking a superfluid with SU(2) internal symmetry in2+1 dimensions breaks parity spontaneously, and introduces parity-odd terms inthe constitutive relations. We show that there are qualitatively differentextensions of the rest frame locking to non-zero velocities. We construct theresulting superfluid hydrodynamics up to the first derivative order. Using anexpansion close to the critical point, we estimate the ratio of the Hallviscosity and the angular momentum density. Our general hydrodynamic resultsare compatible with the holographic p-wave calculations in arXiv:1311.4882.

Odd Parity Transport In Non-Abelian Superfluids From Symmetry Locking