Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

Understand

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion.

• We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field.
• We parameterize the general form of this action at first order in the derivative expansion.
• We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action.