  The exciton Bose liquid (EBL) is a hypothesized phase of bosons in 2+1D which
possesses a dispersion that is gapless along the coordinate axes in momentum
space. The low energy theory of the EBL involves modes on all length scales,
extending all the way down to the lattice spacing. In this note, we discuss an
RG scheme that can be used to address the stability of this and related phases
of matter. We argue that in the absence of an extensively large symmetry group,
realizing the simplest formulation of the EBL always requires fine-tuning.
However, we also argue that the addition of certain marginal interactions can
likely be used to realize a stable phase, without the need for fine-tuning. A
simple generalization to 3+1D is also discussed.
