Stability analysis of the Luttinger liquid fixed-point in metallic nanotubes

We study the stability of a Luttinger liquid in a metallic single-walled nanotube against generic backscattering and Umklapp perturbations. Analizing the renormalization group equations we identify nontrivial particular solutions that lay in the same universality class of the Luttinger liquid. We describe in detail the mechanism of instability generation in that electron liquid and discuss under which conditions it governs the physical properties in the presence of low frequency or temperature cutoffs