  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.
