Symmetric Superfluids

Understand

We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincar\'{e} 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\geq 2 $ spacetime dimensions there are only two possibilities: the Dirac-Born-Infeld theory and Scaling Superfluids with Lagrangian $ (-\partial_{\mu}\phi\partial^{\mu}\phi)^{\alpha}$, for some real $ \alpha$.
• The scaling symmetry present for any $ \alpha $ is further enhanced to the full conformal group only for $ \alpha=D/2 $, and to infinitely many additional generators for $ \alpha=1/2 $.