Indications of a nontrivial vacuum in the effective theory of perfect fluids

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 nontrivial, casting doubts on whether the gradient expansion can provide a good effective field theory for this type of system. The nontrivial 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.

Figure 1

A schematic illustration of a possible vacuum structure of the theory, in terms of a free energy including both microscopic degrees of freedom and macroscopic collective excitations. The left side is the “hydrostatic limit,” where expansions such as [3] lead to a well-behaved effective theory. The right side is a possibly turbulent vacuum where a fraction of the entropy goes into microscopic degrees of freedom. In this figure the free energy corresponds to the coexistence phase of a first order phase transition, but of course other configurations between the two vacua (second order, crossover, critical points and so on) are equally possible. The image on the right was courtesy of SCIDA [16].

Figure 2

The energy density as a function of $a{T}_0$ and the lattice size for ensembles both with and without collective “sound modes” present. Left: Average energy density in lattice units. Right: ratio of average energy density and the $4/3$-power of the lattice-averaged entropy density, $⟨s⟩$.

Figure 3

Plot of the time component of the flow as a function of $a{T}_0$.

Figure 4

Phonon correlators of longitudinal sound modes.

Figure 5

Relative entropy-density correlators. Left: results for two ${16}^4$, $a{T}_0=0.5$ ensembles—one with a sound mode and one without—as a function of time separation (dotted symbols are for negative values). Right: the spatial dependence from the sound-mode ensemble.