Abstract
We consider relativistic non-Abelian superfluids, where the expectation value of the global symmetry currents relate space and internal indices, thus creating a “locked” phase. Locking a superfluid with SU(2) internal symmetry in 2+1 dimensions breaks parity spontaneously, and introduces parity-odd terms in the constitutive relations. We show that there are qualitatively different extensions of the rest frame locking to non-zero velocities. We construct the resulting superfluid hydrodynamics up to the first derivative order. Using an expansion close to the critical point, we estimate the ratio of the Hall viscosity and the angular momentum density. Our general hydrodynamic results are compatible with the holographic p-wave calculations in arXiv:1311.4882.
Highlights
Breaking parity introduces new transport effects in fluid hydrodynamics
We will solve the hydrodynamic equations with external sources to identify the Hall viscosity and angular momentum density in the frame where there is no current J3i = 0,7 which we identify as the ground state of the system
For the metric and gauge field they group into tensor, vector and scalar. Both Hall viscosity coefficients appear from tensor fluctuations, while the angular momentum density has a contribution from the vector fluctuation and a contribution that originates from momentum-dependent fluctuations that mix scalar with vector fluctuations
Summary
Breaking parity introduces new transport effects in fluid hydrodynamics. The parity breaking can be explicit, spontaneous or as a consequence of quantum anomalies, each with its unique signature. An interesting parity-odd transport is the dissipationless Hall viscosity ηH in 2 + 1 fluids [1, 2] It enters in the constitutive relations of the fluid as a term in the stress tensor. The aim of this paper is to study parity-odd transport in superfluid hydrodynamics with spontaneously broken parity, and in particular the general properties of the above relation between the Hall viscosity and the angular momentum density. We will study the hydrodynamics of relativistic non-Abelian superfluids in a symmetry locked phase, that is where the expectation value of the global symmetry currents relate space and internal indices.
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