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The exciton Bose liquid (EBL) is a hypothesized phase of bosons in 2+1D whichpossesses a dispersion that is gapless along the coordinate axes in momentumspace. 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 anRG scheme that can be used to address the stability of this and related phasesof 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 canlikely be used to realize a stable phase, without the need for fine-tuning. Asimple generalization to 3+1D is also discussed.

RG and Stability in the Exciton Bose Liquid