  We develop a low-energy model of a unidirectional Larkin-Ovchinnikov (LO)
state. Because the underlying rotational and translational symmetries are
broken spontaneously, this gapless superfluid is a smectic liquid crystal, that
exhibits fluctuations that are qualitatively stronger than in a conventional
superfluid, thus requiring a fully nonlinear description of its Goldstone
modes. Consequently, at nonzero temperature the LO superfluid is an algebraic
phase even in 3d. It exhibits half-integer vortex-dislocation defects, whose
unbinding leads to transitions to a superfluid nematic and other phases. In 2d
at nonzero temperature, the LO state is always unstable to a charge-4 nematic
superfluid. We expect this superfluid liquid-crystal phenomenology to be
realizable in imbalanced resonant Fermi gases trapped isotropically.
