Bose-Luttinger Liquids

We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub "Bose-Luttinger liquids", which in some respects can be regarded as bosonic versions of Fermi liquids, while in other respects exhibit striking differences. These phases have bosonic analogues of Fermi surfaces, and like Fermi liquids they possess a large number of emergent conservation laws. Unlike Fermi liquids however these phases lack quasiparticles, possess different RG flows, and have correlation functions controlled by a continuously varying exponent $\eta$, which characterizes the anomalous dimension of the bosonic field. We show that when $\eta>1$, these phases are stable with respect to all symmetric perturbations. These theories may be of relevance to several physical situations, including frustrated quantum magnets, rotons in superfluid He, and superconductors with finite-momentum pairing. As a concrete application, we show that coupling a Bose-Luttinger liquid to a conventional Fermi liquid produces a resistivity scaling with temperature as $T^\eta$. We argue that this may provide an explanation for the non-Fermi liquid resistivity observed in the paramagnetic phase of MnSi.