Field theory for a deuteron quantum liquid

Based on general symmetry principles we study an effective Lagrangian for a neutral system of condensed spin-1 deuteron nuclei and electrons, at greater-than-atomic but less-than-nuclear densities. We expect such matter to be present in thin layers within certain low-mass brown dwarfs. It may also be produced in future shock-wave-compression experiments as an effective fuel for laser-induced nuclear fusion. We find a background solution of the effective theory describing a net spin zero condensate of deuterons with their spins aligned and anti-aligned in a certain spontaneously emerged preferred direction. The spectrum of low energy collective excitations contains two spin-waves with linear dispersions - like in antiferromagnets - as well as gapped longitudinal and transverse modes related to the Meissner effect - like in superconductors. We show that counting of the Nambu- Goldstone modes of spontaneously broken internal and space-time symmetries obeys, in a nontrivial way, the rules of the Goldstone theorem for Lorentz non-invariant systems. We discuss thermodynamic properties of the condensate, and its potential manifestation in the low-mass brown dwarfs.