# Symmetric Superfluids

## TL;DR

This paper classifies symmetric superfluids with shift and Poincaré invariance, revealing only two models in higher dimensions and analyzing their symmetries, stability, and coupling constants.

## Contribution

It provides a complete classification of symmetric superfluids with fixed couplings, identifying only Dirac-Born-Infeld and Scaling Superfluids as possibilities in higher dimensions.

## Key findings

- Only two models in D≥2: DBI and Scaling Superfluids.
- Full conformal symmetry occurs at specific scaling exponents.
- Coupling constants are fixed by the speed of sound.

## Abstract

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 $. We discuss the stability of Scaling Superfluids and point out that all coupling constants are determined by the speed of sound.