Using lattice field theory techniques, we investigate the vacuum structure of the field theory corresponding to perfect fluid dynamics in the Lagrangian prescription. We find intriguing, but inconclusive evidence, that the vacuum of such a theory is non-trivial, casting doubts on whether the gradient expansion can provide a good effective field theory for this type of system. The non-trivial vacuum looks like a “turbulent” state where some of the entropy is carried by macroscopic degrees of freedom. We describe further steps to strengthen or falsify this evidence.
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