A new class of "soft" O(N) sigma models

A uni-directional "density" wave order in an isotropic environment is guaranteed (by underlying spontaneously broken rotational symmetry) to display "soft" smectic-like Goldstone modes. Examples of such "soft" states include smectic liquid crystals, putative Fulde-Ferrell-Larkin-Ovchinnikov superfluids, helical states of frustrated bosons and spins. In this talk, I will discuss a new class of fully rotationally invariant O(N) smectic sigma- and associated Ginzburg-Landau models to describe such unusual, strongly fluctuating states, their phase transitions and low energy properties. I will also show that below three dimensions such models display strongly-coupled Goldstone modes tamed by nonlinearities that lead to a critical phase with universal anomalous correlations.