Abstract
We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincaré invariant scalar field theories that have an enlarged set of classically conserved currents at leading order in derivatives. These theories arise in the decoupling limit of the effective field theory of shift-symmetric, single-clock cosmologies and our results pick out all models with couplings fixed by additional symmetry. Remarkably, in D ≥ 2 spacetime dimensions there are only two possibilities: the Dirac-Born-Infeld theory and Scaling Superfluids with Lagrangian (−∂μϕ∂μϕ)α, for some real α. The scaling symmetry present for any α is further enhanced to the full conformal group only for α = D/2, and to infinitely many additional generators for the cuscuton, namely α = 1/2. We discuss the stability of Scaling Superfluids and point out that all coupling constants are determined by the speed of sound.
Highlights
Invariant but allow for this symmetry to be spontaneously broken
These theories arise in the decoupling limit of the effective field theory of shift-symmetric, single-clock cosmologies and our results pick out all models with couplings fixed by additional symmetry
It is perhaps at first surprising to find scaling but not conformal symmetry as is the case for α = D/2, but this is compatible with all results in the literature (e.g. [8,9,10,11,12,13,14]) which rely on linearly realized symmetries
Summary
The first of these commutators tells us that Dis the generator of dilatations while the second tells us that Q transforms under dilatations with scaling weight −∆ This symmetry acts linearly on φ, it acts non-linearly on the Superfluid phonon π and as we shall. The U(1) symmetry Q corresponds to translations in the extra dimension, i.e. Q = PD+1, while the new vector generator Aμ corresponds to Lorentz transformations involving the extra dimension, i.e. Aμ = Mμ(D+1). The non-zero commutators are the generalisation of (2.4) to one extra spatial dimension This theory requires no further discussion but let us mention that higher derivative corrections were considered in [38] and the constraints on the EFT of inflation imposed by the symmetry were considered in [39, 40]
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