We introduce a class of dynamical field theories for $N$-component “Borromean” ($N\ge 3$) supercounterfluid order, naturally formulated in terms of interspecies bosonic fields ${\psi }_{\alpha \beta }$. Their condensation breaks the normal-state ${\left[\mathrm{U}\left(1\right)\right]}^N$ symmetry down to its diagonal U(1) subgroup, thereby encoding the arrest of the net superflow. This approach broadens our understanding of dynamical properties of supercounterfluids, at low energies capturing its universal properties, phase transition, counterflow vortices, and many of its other properties. Such supercounterfluid strikingly exhibits $N$ distinct flavors of energetically stable elementary vortex solutions, despite ${\mathbb{Z}}^{N-1}$ homotopy group of its $N-1$ independent Goldstone modes, with $N-1$ topologically distinct elementary vortex types, obeying modular arithmetic. The model leads to Borromean hydrodynamics as a low-energy theory, reveals the counterflow AC Josephson effect, and generically predicts a first-order character of the phase transitions into Borromean supercounterfluid state in dimensions greater than two.

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• Cold atoms & matter waves
• Effective field theory
• Goldstone bosons
• Superfluidity
• U(N) symmetry